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The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
The optical conductivity of the one-band Hubbard model is calculated using the 'Dynamical Cluster Approximation' implementation of dynamical mean field theory for parameters appropriate to high temperature copper-oxide superconductors. The…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
We study electron correlations in the half-filled Hubbard model on two-dimensional Penrose lattice. Applying the real-space dynamical mean-field theory to large clusters, we discuss how low-temperature properties are affected by the…
Near-term quantum processors are limited in terms of the number of qubits and gates they can afford. They nevertheless give unprecedented access to programmable quantum systems that can efficiently, although imperfectly, simulate quantum…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…
Cluster Dynamical Mean Field Theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean field theory, PCDMFT, is presented. The…
The enigma of unconventional superconductivity in doped cuprates presents a formidable challenge in the realm of condensed matter physics. Recent findings of strong near-neighbor attractions in one-dimensional cuprate chains suggest a new…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…
Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and…
Frustrated spin models may lead to the formation of both classical non-collinear spin structures and unique quantum phases including highly entangled quantum spin liquids. Here, we study the entanglement and spatial quantum correlations in…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
A method of cluster diagonalization in a systematically expanded Hilbert space is described. We discuss some applications of this procedure to models of high-T_c superconductors, like the t - J and one and three bands Hubbard models in two…
The Fermi-Hubbard model is the starting point for the simulation of many strongly correlated materials, including high-temperature superconductors, whose modelling is a key motivation for the construction of quantum simulation and computing…
A general technique is presented for constructing a quantum theory of a finite number of interacting particles satisfying Poincar\'e invariance, cluster separability, and the spectral condition. Irreducible representations and…
The dynamics of quantum correlations are central to understanding many physical properties of quantum systems. Here we experimentally study the correlation dynamics via two-particle quantum walks in superconducting Bose-Hubbard qutrit…
In the present paper we examine the relationship between several type $A$ cluster theories and structures. We define a 2D geometric model of a cluster theory, which generalizes cluster algebras from surfaces, and encode several existing…