Related papers: R\'enyi free energy and variational approximations…
We study the statistical physics of the classical Ising model in the so-called $\alpha$-R\'enyi ensemble, a finite-temperature thermal state approximation that minimizes a modified free energy based on the $\alpha$-R\'enyi entropy. We begin…
Preparing thermal equilibrium states is an essential task for finite-temperature quantum simulations. In statistical mechanics, microstates in thermal equilibrium can be obtained from statistical ensembles. To date, numerous ensembles have…
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…
Studying finite-temperature properties with tensor networks is notoriously difficult, especially at low temperatures, due to the rapid growth of entanglement and the complexity of thermal states. Existing methods like purification and…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
Thermal pure state algorithms, which employ pure quantum states representing thermal equilibrium states instead of statistical ensembles, are useful both for numerical simulations and for theoretical analysis of thermal states. However,…
We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that…
We introduce a tensor network method for approximating thermal equilibrium states of quantum many-body systems at low temperatures. Whereas the usual approach starts from infinite temperature and evolves the state in imaginary time (toward…
We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite temperature properties of quantum systems are derived without the need of statistical mechanics ensembles, but instead using…
Despite being a well-established operational approach to quantify entanglement, R\'enyi entropy calculations have been plagued by their computational complexity. We introduce here a theoretical framework based on an optimal thermodynamic…
State space geometry is obtained for the one dimensional Blume Emery Griffiths model and the associated scalar curvature(s) investigated for various parameter regimes, including the Blume-Capel limit and the Griffiths model limit. For the…
We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to…
We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature,…
We study the local and (bipartite) entanglement R\'enyi entropies of the free Fermi gas in multi-dimensional Euclidean space $\mathbb{R}^d$ in thermal equilibrium. We prove positivity of the entanglement entropies with R\'enyi index…
An estimator for the dynamical temperature in an arbitrary ensemble is derived in the framework of Bayesian statistical mechanics and the maximum entropy principle. We test this estimator numerically by a simulation of the two-dimensional…
The R\'{e}nyi statistics is applied for a description of finite size effects in the 1D Ising model. We calculate the internal energy of the spin chain and the system temperature using the R\'{e}nyi distribution and postulate them to be…
We calculate thermal corrections to R\'{e}nyi entropies for free massless fermions on a sphere. More specifically, we take a free fermion on $\mathbb{R}\times\mathbb{S}^{d-1}$ and calculate the leading thermal correction to the R\'{e}nyi…
One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the tensor network approximations to thermal…
A theory of thermodynamics has been recently formulated and derived on the basis of R\'enyi entropy and its relative versions. In this framework, we define the concepts of partition function, internal energy and free energy, and fundamental…
Method of random phase product state (RPPS) is proposed to calculate canonical ensemble average of quantum systems described with matrix product states and also with tensor network states in general. The RPPS method is an extension of the…