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We discuss possible patterns of electron fractionalization in strongly interacting electron systems. A popular possibility is one in which the charge of the electron has been liberated from its Fermi statistics. Such a fractionalized phase…
As computers get faster, researchers -- not hardware or algorithms -- become the bottleneck in scientific discovery. Computational study of colloidal self-assembly is one area that is keenly affected: even after computers generate massive…
Strongly interacting electron systems can provide insight into quantum many-body phenomena, such as Mott insulating behavior and spin liquidity, facilitating semiconductor optimization. The Fermi-Hubbard model is the prototypical model used…
Competition between superconductivity and charge order is a recurring theme in contemporary condensed matter physics. This is quintessentially captured in the attractive Hubbard model, a simple theoretical model where the competition can be…
We consider ultracold matter of spin-2 atoms in optical lattices. We derive an effective Hamiltonian for the studies of spin ordering in Mott states and investigate hyperfine spin correlations. Particularly, we diagonalize the Hamiltonian…
We study an extended Hubbard model in the limit of infinite dimensions and its zero dimensional counterpart, a generalized asymmetric Anderson model. In the impurity model we find three kinds of mixed valence states: a) the usual strong…
Monitoring complex systems results in massive multivariate time series data, and anomaly detection of these data is very important to maintain the normal operation of the systems. Despite the recent emergence of a large number of anomaly…
We apply a variational Ansatz based on neural networks to the problem of spin-$1/2$ fermions in a harmonic trap interacting through a short distance potential. We showed that standard machine learning techniques lead to a quick convergence…
We compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an ansatz for the…
By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ…
A mixture of spin-polarized light and heavy fermionic atoms on a finite size 2D optical lattice is considered at various temperatures and values of the coupling between the two atomic species. In the case, where the heavy atoms are immobile…
We show how spin-spin correlations, detected in a non-destructive way via spatially resolved quantum polarization spectroscopy, strongly characterize various phases realized in trapped ultracold fermionic atoms. Polarization degrees of…
We develop a theory of a hybrid state, where quasi-particles coexist with strong collective modes, taking as a starting point a model of infinitely many 1D Mott insulators coupled by a weak interchain tunneling. This state exists at an…
An exactly soluble one-dimensional model of electrons interacting with order parameter fluctations associated with short-range order is considered. The energy and momentum dependence of the electronic self energy and spectral function are…
The underlying physics behind an experimental observation often lacks a simple analytical description. This is especially the case for scanning probe microscopy techniques, where the interaction between the probe and the sample is…
Recently, there has been an increased interest in the application of machine learning (ML) techniques to a variety of problems in condensed matter physics. In this regard, of particular significance is the characterization of simple and…
The ability to detect macroscopic changes is important for probing the behaviors of experimental many-body systems from the classical to the quantum realm. Although abrupt changes near phase boundaries can easily be detected, subtle…
Traditionally one and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient because higher-order…
Theoretical ideas and experimental results concerning high temperature superconductors are reviewed. Special emphasis is given to calculations carried out with the help of computers applied to models of strongly correlated electrons…
A model is introduced describing the interplay between superconductivity and spin-ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions,…