Hermitian and non-Hermitian thermal Hamiltonians

Adrian E. Feiguin; Israel Klich

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arXiv · 1308.0756

Hermitian and non-Hermitian thermal Hamiltonians

Adrian E. Feiguin·Israel Klich

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Abstract

Thermal density matrices can be described by a pure quantum state within the thermofield formalism. Here we show how to construct a class of Hamiltonians realizing a thermofield state as their ground state. These Hamiltonians are frustration-free, and can be Hermitian or non-Hermitian, allowing one to use ground-state methods to understand the thermodynamic properties of the system. In particular this approach gives an explicit mapping of thermal phase transitions into quantum phase transitions. In the non-Hermitian case, the quantum phase transition is not accompanied by a change in the spectrum of the Hamiltonian, which remains gapped. We illustrate these ideas for the classical 2D Ising model.

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Adrian E. Feiguin, Israel Klich. 2013-08-03. Hermitian and non-Hermitian thermal Hamiltonians. https://arxiv.org/abs/1308.0756

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