Related papers: Finding and proving the exact ground state of a ge…
Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions,…
Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices…
Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP-hard in the most general case. Owing to the specific structure…
We introduce a method based on semidefinite programming that produces rigorous two-sided bounds on ground state energy densities and correlation functions of translation-invariant classical spin models on infinite lattices. In this method,…
For many systems with quenched disorder the study of ground states can crucially contribute to a thorough understanding of the physics at play, be it for the critical behavior if that is governed by a zero-temperature fixed point or for…
On the grounds of a Feynman-Kac--type formula for Hamiltonian lattice systems we derive analytical expressions for the matrix elements of the evolution operator. These expressions are valid at long times when a central limit theorem…
As a means to solve optimization problems using quantum computers, the problem is typically recast into a Ising spin model whose ground-state is the solution of the optimization problem. An alternative to the Ising formulation is the…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
We investigate the application of graph-cut methods for the study of the critical behaviour of the two-dimensional random-field Ising model. We focus on exact ground-state calculations, crossing the phase boundary of the model at zero…
We characterize the set of ground states that can be synthesized by classical 2-body Ising Hamiltonians. We then construct simple Ising planar blocks that simulates efficiently a universal set of logic gates and connections, and hence any…
We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state,…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to…
Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed…
In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state…
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…
An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising…
In this article, new results are presented for the zero-temperature ground-state properties of the spin-half transverse Ising model on various lattices using three different approximate techniques. These are, respectively, the coupled…
We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac,…