Insights into phase transitions and entanglement from density functional theory

Bo-Bo Wei

doi:10.1088/1367-2630/18/11/113035

Abstract

Density functional theory (DFT) has met great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that DFT could shed light on phase transitions and entanglement at finite temperatures. Specifically, we show that the equilibrium state of an interacting quantum many-body system which is in thermal equilibrium with a heat bath at a fixed temperature is a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters respectively. This insight from DFT enables us to express the average value of any physical observable and any entanglement measure as a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters. Since phase transitions are marked by the nonanalytic behavior of free energy with respect to control parameters, the physical quantities and entanglement measures may present nonanalytic behavior at critical point inherited from their dependence on the first derivative of free energy. We use two solvable models to demonstrate these ideas. These results give new insights for phase transitions and provide new profound connections between entanglement and phase transitions in interacting quantum many-body physics.

Highlights

The electronic density functional theory (DFT) developed by Hohenberg and Kohn[1] and Kohn and Sham [2] in 19641965 has shown tremendous success in solid state physics, quantum chemistry and in computational material sciences [3, 4]
In this work we show that density functional theory provides insights for finite temperature phase transitions
We prove that the equilibrium state of a quantum many-body system, which is in thermal equilibrium with a heat bath, is a universal functional of the first derivative of the free energy with respect to the control parameters

Summary

INTRODUCTION

The electronic density functional theory (DFT) developed by Hohenberg and Kohn[1] and Kohn and Sham [2] in 19641965 has shown tremendous success in solid state physics, quantum chemistry and in computational material sciences [3, 4]. We prove that the equilibrium state of a quantum many-body system, which is in thermal equilibrium with a heat bath, is a universal functional of the first derivative of the free energy with respect to the control parameters. This finding explains how the non-analytic behavior of free energy at critical point affects the expectation values of physical observable at phase transition point. Since entanglement in quantum many-body systems is a functional of expectation value of observable, the finding introduces a direct link between entanglement and the first derivatives of free energy, leading to a deep connection between entanglement and phase transitions. VI we study an experimentally relevant model to demonstrate our central ideas and we give a summary

INSIGHT INTO PHASE TRANSITIONS FROM DENSITY FUNCTIONAL THEORY

RELATIONS BETWEEN ENTANGLEMENT AND PHASE TRANSITIONS FROM DENSITY FUNCTIONAL

MODEL STUDY

SUMMARY