Statistical Mechanics
A proof of the Bloch theorem for lattice models (1904.02700v1)
Haruki Watanabe
2019-04-04
The Bloch theorem is a powerful theorem stating the absence of nonzero expectation value of the current operator associated with a conserved U(1) charge in the ground state. This short note presents a simple yet rigorous version of the proof for general lattice models. Our discussion clarifies the relation to the twist operator widely used in the context of the Lieb-Schultz-Mattis theorem.
Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics (1904.02696v1)
Bruno Bertini, Lorenzo Piroli, Márton Kormos
2019-04-04
The semiclassical approach introduced by Sachdev and collaborators proved to be extremely successful in the study of quantum quenches in massive field theories, both in homogeneous and inhomogeneous settings. While conceptually very simple, this method allows one to obtain analytic predictions for several observables when the density of excitations produced by the quench is small. At the same time, a novel generalized hydrodynamic (GHD) approach, which captures exactly many asymptotic features of the integrable dynamics, has recently been introduced. Interestingly, also this theory has a natural interpretation in terms of semiclassical particles and it is then natural to compare the two approaches. This is the objective of this work: we carry out a systematic comparison between the two methods in the prototypical example of the sine-Gordon field theory. In particular, we study the "bipartitioning protocol" where the two halves of a system initially prepared at different temperatures are joined together and then left to evolve unitarily with the same Hamiltonian. We identify two different limits in which the semiclassical predictions are analytically recovered from GHD: a particular non-relativistic limit and the low temperature regime. Interestingly, the transport of topological charge becomes sub-ballistic in these cases. Away from these limits we find that the semiclassical predictions are only approximate and, in contrast to the latter, the transport is always ballistic. This statement seems to hold true even for the so-called "hybrid" semiclassical approach, where finite time DMRG simulations are used to describe the evolution in the internal space.
Determination of the Critical Manifold Tangent Space and Curvature with Monte Carlo Renormalization Group (1903.08231v2)
Yantao Wu, Roberto Car
2019-03-19
We show that the critical manifold of a statistical mechanical system around a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with Variational Monte Carlo Renormalization Group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. We study the isotropic and anisotropic Ising model on a two-dimensional square lattice, and the isotropic Ising model on a cubic lattice to illustrate the method.
The Tangent Space to the Manifold of Critical Classical Hamiltonians Representable by Tensor Networks (1903.12137v2)
Yantao Wu
2019-03-28
We introduce a scheme to perform Monte Carlo Renormalization Group with the coupling constants of the system Hamiltonian encoded in a tensor network. With this scheme we compute the tangent space to the critical manifold at the nearest-neighbor critical coupling for three models: the two and three dimensional Ising models and the two dimensional three-state Potts model.
Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source (1901.02002v4)
Serge N. Gavrilov, Anton M. Krivtsov
2019-01-07
We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system of stochastic ordinary differential equations. We perform a continualization procedure and derive an infinite system of linear partial differential equations for covariance variables. The most important results of the paper are the deterministic differential-difference equation describing non-stationary heat propagation in the lattice and the analytical formula in the integral form for its steady-state solution describing kinetic temperature distribution caused by a point heat source of a constant intensity. The comparison between numerical solution of stochastic equations and obtained analytical solution demonstrates a very good agreement everywhere except for the main diagonals of the lattice (with respect to the point source position), where the analytical solution is singular.
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