Quantum phase transitions without thermodynamic limits

Abstract

A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function. It is demonstrated that generic quantum systems therefore exhibit second-order (continuous) phase transitions at finite temperatures.

4 Pages, further references added

References in corpus (5)

• Canonical Typicality
• Phase transitions and topology changes in configuration space
• Unattainability of a purely topological criterion for the existence of a phase transition for non-confining potentials
• On the mean-field spherical model
• Topological approach to phase transitions and inequivalence of statistical ensembles

Cited by in corpus (16)

• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Phase transitions and configuration space topology
• Excited-state quantum phase transitions
• Typical state of an isolated quantum system with fixed energy and unrestricted participation of eigenstates
• Concentration of measure for quantum states with a fixed expectation value
• Nonanalyticities of the entropy induced by saddle points of the potential energy landscape
• Quantum Fluctuation Relations for Ensembles of Wave Functions
• Excited State Quantum Phase Transitions Studied from a Non-Hermitian Perspective
• Thermodynamics of Quantum Heat Bath
• Topological Theory of Phase Transitions
• Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory
• Generalized quantum microcanonical ensemble from random matrix product states
• Probability density of quantum expectation values
• Heat capacity for systems with excited-state quantum phase transitions
• Beyond quantum microcanonical statistics
• Comment on "Typicality for Generalized Microcanonical Ensemble"