Related papers: Efficient simulation of infinite tree tensor netwo…
We study the Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods.…
Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator $e^{-\beta H}$ for a two-dimensional (2D) lattice system with a Hamiltonian $H$ can be represented by a…
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice…
We study the emergence of confinement in the transverse field Ising model on a decorated hexagonal lattice. Using an infinite tensor network state optimised with belief propagation we show how a quench from a broken symmetry state leads to…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely…
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…
We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a…
It is known that for the Heisenberg XXZ spin-$\frac{1}{2}$ chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D…
In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in…
An efficient algorithm is developed for quantum spin tubes in the context of the tensor network representations. It allows to efficiently compute the ground-state fidelity per lattice site, which in turn enables us to identify quantum…
We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which…
We establish an intriguing connection between quantum phase transitions and bifurcations in the ground-state fidelity per lattice site, and construct the universal order parameter for quantum Ising model in a transverse magnetic field on an…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
We study the P"oschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms…
The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the…