Related papers: Phase boundary location with information-theoretic…
Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…
We propose a novel algorithm with a modified Tucker decomposition for tensor network that allows for efficiently and precisely calculating the ground state and thermodynamic properties of two-dimensional (2D) quantum spin lattice systems,…
We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…
The phase transition occurring in a square 2-D spin lattice governed by an anisotropic Heisenberg Hamiltonian has been studied according to two recently proposed methods. The first one, the Dressed Cluster Method, provides excellent…
Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information…
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor…
Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network…
Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic…
In this paper, we propose a novel machine learning method based on an adaptive tensor neural network subspace for solving quasiperiodic elliptic problems. To this end, we first provide a theoretical analysis of the associated quasiperiodic…
We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) interactions. Using the tensor renormalization-group method augmented by higher-order singular value decompositions, we…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point…
The critical phenomena of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ are investigated using the techniques of neural networks (NN). In particular, an unconventional supervised NN which…
The accurate prediction of phase diagrams is of central importance for both the fundamental understanding of materials as well as for technological applications in material sciences. However, the computational prediction of the relative…
In this work, we first propose a diffuse interface model for simulating N phase flows with solid liquid phase change. In this model, a phase field approach is adopted to capture multiphase fluid interfaces, and an enthalpy based formulation…
We present a method for joint phase identification and topology recovery in unbalanced three phase radial networks using only voltage measurements. By recovering phases and topology jointly, we utilize all three phase voltage measurements…
We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to the study of the three-dimensional antiferromagnetic q-state Potts models on a simple cubic lattice. We systematically study the phase transition of the models with…
We study the Riemannian geometry of the Deep Linear Network (DLN) as a foundation for a thermodynamic description of the learning process. The main tools are the use of group actions to analyze overparametrization and the use of Riemannian…
The flow equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one dimensional model with power-law decaying hoppings. This model presents a…