A parallel computing method for the higher order tensor renormalization group
In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract...
Ausführliche Beschreibung
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| Autor*in: |
Yamashita, Takumi [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Sa1070 Epidemiology of Gastroesophageal Reflux (GERD) Symptoms in Mexico. A Nationwide Population Based Study - Remes-Troche, Jose Maria ELSEVIER, 2014, an international journal for computational physics and physical chemistry, Amsterdam |
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| Übergeordnetes Werk: |
volume:278 ; year:2022 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.cpc.2022.108423 |
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| 245 | 1 | 0 | |a A parallel computing method for the higher order tensor renormalization group |
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| 520 | |a In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . | ||
| 520 | |a In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . | ||
| 650 | 7 | |a Parallel computing |2 Elsevier | |
| 650 | 7 | |a The higher order tensor renormalization group |2 Elsevier | |
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10.1016/j.cpc.2022.108423 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001828.pica (DE-627)ELV057976589 (ELSEVIER)S0010-4655(22)00142-4 DE-627 ger DE-627 rakwb eng 610 VZ 570 VZ BIODIV DE-30 fid 35.70 bkl 42.12 bkl 42.15 bkl Yamashita, Takumi verfasserin aut A parallel computing method for the higher order tensor renormalization group 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . Parallel computing Elsevier The higher order tensor renormalization group Elsevier Tensor network Elsevier Sakurai, Tetsuya oth Enthalten in North Holland Publ. Co Remes-Troche, Jose Maria ELSEVIER Sa1070 Epidemiology of Gastroesophageal Reflux (GERD) Symptoms in Mexico. A Nationwide Population Based Study 2014 an international journal for computational physics and physical chemistry Amsterdam (DE-627)ELV012614815 volume:278 year:2022 pages:0 https://doi.org/10.1016/j.cpc.2022.108423 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_105 35.70 Biochemie: Allgemeines VZ 42.12 Biophysik VZ 42.15 Zellbiologie VZ AR 278 2022 0 |
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10.1016/j.cpc.2022.108423 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001828.pica (DE-627)ELV057976589 (ELSEVIER)S0010-4655(22)00142-4 DE-627 ger DE-627 rakwb eng 610 VZ 570 VZ BIODIV DE-30 fid 35.70 bkl 42.12 bkl 42.15 bkl Yamashita, Takumi verfasserin aut A parallel computing method for the higher order tensor renormalization group 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . Parallel computing Elsevier The higher order tensor renormalization group Elsevier Tensor network Elsevier Sakurai, Tetsuya oth Enthalten in North Holland Publ. Co Remes-Troche, Jose Maria ELSEVIER Sa1070 Epidemiology of Gastroesophageal Reflux (GERD) Symptoms in Mexico. A Nationwide Population Based Study 2014 an international journal for computational physics and physical chemistry Amsterdam (DE-627)ELV012614815 volume:278 year:2022 pages:0 https://doi.org/10.1016/j.cpc.2022.108423 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_105 35.70 Biochemie: Allgemeines VZ 42.12 Biophysik VZ 42.15 Zellbiologie VZ AR 278 2022 0 |
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10.1016/j.cpc.2022.108423 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001828.pica (DE-627)ELV057976589 (ELSEVIER)S0010-4655(22)00142-4 DE-627 ger DE-627 rakwb eng 610 VZ 570 VZ BIODIV DE-30 fid 35.70 bkl 42.12 bkl 42.15 bkl Yamashita, Takumi verfasserin aut A parallel computing method for the higher order tensor renormalization group 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . Parallel computing Elsevier The higher order tensor renormalization group Elsevier Tensor network Elsevier Sakurai, Tetsuya oth Enthalten in North Holland Publ. Co Remes-Troche, Jose Maria ELSEVIER Sa1070 Epidemiology of Gastroesophageal Reflux (GERD) Symptoms in Mexico. A Nationwide Population Based Study 2014 an international journal for computational physics and physical chemistry Amsterdam (DE-627)ELV012614815 volume:278 year:2022 pages:0 https://doi.org/10.1016/j.cpc.2022.108423 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_105 35.70 Biochemie: Allgemeines VZ 42.12 Biophysik VZ 42.15 Zellbiologie VZ AR 278 2022 0 |
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10.1016/j.cpc.2022.108423 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001828.pica (DE-627)ELV057976589 (ELSEVIER)S0010-4655(22)00142-4 DE-627 ger DE-627 rakwb eng 610 VZ 570 VZ BIODIV DE-30 fid 35.70 bkl 42.12 bkl 42.15 bkl Yamashita, Takumi verfasserin aut A parallel computing method for the higher order tensor renormalization group 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . Parallel computing Elsevier The higher order tensor renormalization group Elsevier Tensor network Elsevier Sakurai, Tetsuya oth Enthalten in North Holland Publ. Co Remes-Troche, Jose Maria ELSEVIER Sa1070 Epidemiology of Gastroesophageal Reflux (GERD) Symptoms in Mexico. A Nationwide Population Based Study 2014 an international journal for computational physics and physical chemistry Amsterdam (DE-627)ELV012614815 volume:278 year:2022 pages:0 https://doi.org/10.1016/j.cpc.2022.108423 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_105 35.70 Biochemie: Allgemeines VZ 42.12 Biophysik VZ 42.15 Zellbiologie VZ AR 278 2022 0 |
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10.1016/j.cpc.2022.108423 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001828.pica (DE-627)ELV057976589 (ELSEVIER)S0010-4655(22)00142-4 DE-627 ger DE-627 rakwb eng 610 VZ 570 VZ BIODIV DE-30 fid 35.70 bkl 42.12 bkl 42.15 bkl Yamashita, Takumi verfasserin aut A parallel computing method for the higher order tensor renormalization group 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . Parallel computing Elsevier The higher order tensor renormalization group Elsevier Tensor network Elsevier Sakurai, Tetsuya oth Enthalten in North Holland Publ. Co Remes-Troche, Jose Maria ELSEVIER Sa1070 Epidemiology of Gastroesophageal Reflux (GERD) Symptoms in Mexico. A Nationwide Population Based Study 2014 an international journal for computational physics and physical chemistry Amsterdam (DE-627)ELV012614815 volume:278 year:2022 pages:0 https://doi.org/10.1016/j.cpc.2022.108423 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_40 GBV_ILN_105 35.70 Biochemie: Allgemeines VZ 42.12 Biophysik VZ 42.15 Zellbiologie VZ AR 278 2022 0 |
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a parallel computing method for the higher order tensor renormalization group |
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A parallel computing method for the higher order tensor renormalization group |
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In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . |
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In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . |
| abstract_unstemmed |
In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional ( d ≥ 2 ) simple lattice model. Sequential computation of the HOTRG requires O ( χ 4 d − 1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O ( χ 2 d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3 , computational cost in each process is reduced to O ( χ 4 d − 3 ) and memory space requirement in each process is kept to be O ( χ 2 d − 1 ) . |
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A parallel computing method for the higher order tensor renormalization group |
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