Related papers: Preserving Hamiltonian Locality in Real-Space Coar…
Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between…
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework…
Long-range quantum lattice systems often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent…
Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system, or has to artificially break certain…
Quantum criticality has received extensive attention due to its ability to significantly enhance quantum sensing. But its realization and control in many-body quantum systems remain challenging. We present an effective scheme to simulate…
We derive a widely-applicable first principles approach for determining two-body, static effective interactions for low-energy Hamiltonians with quantitative accuracy. The algebraic construction rigorously conserves all instantaneous…
We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive…
In this paper we present a simple, yet typical simulation in statistical physics, consisting of large scale Monte Carlo simulations followed by an involved statistical analysis of the results. The purpose is to provide an example…
In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open…
We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…
We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
The COntractor REnormalization group (CORE) method, a new approach to solving Hamiltonian lattice systems, is presented. The method defines a systematic and nonperturbative means of implementing Kadanoff-Wilson real-space renormalization…
Quantum phase transitions driven by electronic correlations are central to understanding the physics of graphene and related two-dimensional materials. A paradigmatic example is the semimetal-to-Mott-insulator transition on the honeycomb…
Machine learning interatomic potentials (MLIPs) have substantially advanced atomistic simulations in materials science and chemistry by balancing accuracy and computational efficiency. While leading MLIPs rely on representing atomic…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
The self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of devised simulation method is the artificial dynamics consisting of the single-spin-flip algorithm of Metropolis…
Systems exhibiting the Hilbert-space fragmentation are nonergodic, and their Hamiltonians decompose into exponentially many blocks in the computational basis. In many cases, these blocks can be labeled by eigenvalues of statistically…
Given the fundamental importance of combinatorial optimization across many diverse application domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better…
Random binning features, introduced in the seminal paper of Rahimi and Recht (2007), are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way…