Hermitian and non-Hermitian thermal Hamiltonians

TL;DR

This paper introduces a class of Hermitian and non-Hermitian Hamiltonians whose ground states represent thermal states, enabling the study of thermal phase transitions through quantum ground-state methods, with applications demonstrated on the 2D Ising model.

Contribution

It constructs frustration-free Hamiltonians that encode thermal states as ground states, bridging thermal and quantum phase transitions, including non-Hermitian cases.

Findings

Ground states of these Hamiltonians correspond to thermal density matrices.

Non-Hermitian Hamiltonians exhibit quantum phase transitions without spectral gap closing.

Application to the 2D Ising model illustrates the approach.

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.