Low temperature phase diagrams for quantum perturbations of classical spin systems
Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Borgs, C. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1996 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 1996 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 181(1996), 2 vom: Nov., Seite 409-446 |
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| Übergeordnetes Werk: |
volume:181 ; year:1996 ; number:2 ; month:11 ; pages:409-446 |
| Links: |
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| DOI / URN: |
10.1007/BF02101010 |
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| Katalog-ID: |
OLC2038866961 |
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| 520 | |a Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. | ||
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10.1007/BF02101010 doi (DE-627)OLC2038866961 (DE-He213)BF02101010-p DE-627 ger DE-627 rakwb eng 530 510 VZ Borgs, C. verfasserin aut Low temperature phase diagrams for quantum perturbations of classical spin systems 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. Quantum System Quantum Computing Spin System Subsequent Paper Zero Temperature Kotecký, R. aut Ueltschi, D. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 181(1996), 2 vom: Nov., Seite 409-446 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:181 year:1996 number:2 month:11 pages:409-446 https://doi.org/10.1007/BF02101010 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 181 1996 2 11 409-446 |
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10.1007/BF02101010 doi (DE-627)OLC2038866961 (DE-He213)BF02101010-p DE-627 ger DE-627 rakwb eng 530 510 VZ Borgs, C. verfasserin aut Low temperature phase diagrams for quantum perturbations of classical spin systems 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. Quantum System Quantum Computing Spin System Subsequent Paper Zero Temperature Kotecký, R. aut Ueltschi, D. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 181(1996), 2 vom: Nov., Seite 409-446 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:181 year:1996 number:2 month:11 pages:409-446 https://doi.org/10.1007/BF02101010 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 181 1996 2 11 409-446 |
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10.1007/BF02101010 doi (DE-627)OLC2038866961 (DE-He213)BF02101010-p DE-627 ger DE-627 rakwb eng 530 510 VZ Borgs, C. verfasserin aut Low temperature phase diagrams for quantum perturbations of classical spin systems 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. Quantum System Quantum Computing Spin System Subsequent Paper Zero Temperature Kotecký, R. aut Ueltschi, D. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 181(1996), 2 vom: Nov., Seite 409-446 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:181 year:1996 number:2 month:11 pages:409-446 https://doi.org/10.1007/BF02101010 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 181 1996 2 11 409-446 |
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10.1007/BF02101010 doi (DE-627)OLC2038866961 (DE-He213)BF02101010-p DE-627 ger DE-627 rakwb eng 530 510 VZ Borgs, C. verfasserin aut Low temperature phase diagrams for quantum perturbations of classical spin systems 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. Quantum System Quantum Computing Spin System Subsequent Paper Zero Temperature Kotecký, R. aut Ueltschi, D. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 181(1996), 2 vom: Nov., Seite 409-446 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:181 year:1996 number:2 month:11 pages:409-446 https://doi.org/10.1007/BF02101010 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 181 1996 2 11 409-446 |
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10.1007/BF02101010 doi (DE-627)OLC2038866961 (DE-He213)BF02101010-p DE-627 ger DE-627 rakwb eng 530 510 VZ Borgs, C. verfasserin aut Low temperature phase diagrams for quantum perturbations of classical spin systems 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1996 Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. Quantum System Quantum Computing Spin System Subsequent Paper Zero Temperature Kotecký, R. aut Ueltschi, D. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 181(1996), 2 vom: Nov., Seite 409-446 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:181 year:1996 number:2 month:11 pages:409-446 https://doi.org/10.1007/BF02101010 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 181 1996 2 11 409-446 |
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low temperature phase diagrams for quantum perturbations of classical spin systems |
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Low temperature phase diagrams for quantum perturbations of classical spin systems |
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Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. © Springer-Verlag 1996 |
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Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. © Springer-Verlag 1996 |
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Abstract We consider a quantum spin system with Hamiltonian$$H = H^{(0)} + \lambda V,$$ whereH(0) is diagonal in a basis ∣s〉=⊗x∣sx〉 which may be labeled by the configurationss={$ s_{x} $} of a suitable classical spin system on $ ℤ^{d} $,$$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH(0)(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH(0), provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper. © Springer-Verlag 1996 |
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