Rényi entropy of quantum anharmonic chain at non-zero temperature
arXiv:2303.04768 · doi:10.1103/PhysRevB.108.245121
Abstract
The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the Rényi entropy is a precious tool to characterize the phase diagram of critical systems not only around the QCP but also away from it, thanks to its capability to detect the emergence of local order at finite temperature. For an efficient evaluation of the Rényi entropy, we introduce a new algorithm based on a path integral Langevin dynamics combined with a previously proposed thermodynamic integration method built on regularized paths. We apply this framework to study the critical behavior of a linear chain of anharmonic oscillators, a particular realization of the model. We fully resolved its phase diagram, as a function of both temperature and interaction strength. At finite temperature, we find a sequence of three regimes - para, disordered and quasi long-range ordered -, met as the interaction is increased. The Rényi entropy divergence coincides with the crossover between the para and disordered regime, which shows no temperature dependence. The occurrence of quasi long-range order, on the other hand, is temperature dependent. The two crossover lines merge in proximity of the QCP, at zero temperature, where the Rényi entropy is sharply peaked. Via its subsystem-size scaling, we confirm that the transition belongs to the two-dimensional Ising universality class. This phenomenology is expected to happen in all -like systems, as well as in the elusive water ice transition across phases VII, VIII and X.
11 + 4 pages, 12 figures
References in corpus (19)
- Area laws in quantum systems: mutual information and correlations
- Quantum magnetism and criticality
- Quantum Criticality
- How to remove the spurious resonances from ring polymer molecular dynamics
- Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model
- From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics
- Stable liquid Hydrogen at high pressure by a novel ab-initio molecular dynamics
- Numerical study of entanglement entropy in SU(2) lattice gauge theory
- Spread of entanglement in a Sachdev-Ye-Kitaev chain
- Theory of the nodal nematic quantum phase transition in superconductors
- Finite Temperature Critical Behavior of Mutual Information
- Renyi Entropy of the Interacting Fermi Liquid
- Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
- An improved lattice measurement of the critical coupling in phi^4_2 theory
- Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
- A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
- A quantum phase transition in the one-dimensional water chain
- Same and interconvertible high-pressure ice phases
- Quantum Rényi entropy by optimal thermodynamic integration paths