arXiv subjects

Richard T. Scalettar

Publications and source records attributed to Richard T. Scalettar.

At least 37 records · Page 2Linked to original sources

arXiv2023

Metal-insulator transition and magnetism of SU(3) fermions in the square lattice

We study the SU(3) symmetric Fermi-Hubbard model (FHM) in the square lattice at $1/3$-filling using numerically exact determinant quantum Monte Carlo (DQMC) and numerical linked-cluster expansion (NLCE) techniques. We present the different regimes of the model in the $T-U$ plane, which are characterized by local and short-range correlations, and capture signatures of the metal-insulator transition and magnetic crossovers. These signatures are detected as the temperature scales characterizing the rise of the compressibility, and an interaction-dependent change in the sign of the diagonal spin-spin correlation function. The analysis of the compressibility estimates the location of the metal-insulator quantum critical point at $U_c/t \sim 6$, and provides a temperature scale for observing Mott physics at finite-$T$. Furthermore, from the analysis of the spin-spin correlation function we observe that for $U/t \gtrsim6$ and $T \sim J = 4t^2/U$ there is a development of a short-range two sublattice (2-SL) antiferromagnetic structure, as well as an emerging three sublattice (3-SL) antiferromagnetic structure as the temperature is lowered below $T/J \lesssim 0.57$. This crossover from 2-SL to 3-SL magnetic ordering agrees with Heisenberg limit predictions, and has observable effects on the density of on-site pairs. Finally, we describe how the features of the regimes in the $T$-$U$ plane can be explored with alkaline-earth-like atoms in optical lattices with currently-achieved experimental techniques and temperatures. The results discussed in this manuscript provide a starting point for the exploration of the SU(3) FHM upon doping.

cond-mat.quant-gas↗

arXiv2023

Frustration- and doping-induced magnetism in a Fermi-Hubbard simulator

Geometrical frustration in strongly correlated systems can give rise to a plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids. Promising candidate materials for such phases can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions $U/t \sim 9$, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120$^{\circ}$ spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices and realizing t-t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials.

cond-mat.quant-gas↗

arXiv2023

Finite-Temperature Quantum Matter with Rydberg or Molecule Synthetic Dimensions

Synthetic dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases - two are localized in the synthetic dimension, predicted as zero-temperature ground states in Refs. [Sci. Rep., 8, 1 (2018) and Phys. Rev. A 99, 013624 (2019)], and a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength, for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tri-critical point on the phase boundary. By examining the dependence of the tri-critical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.

cond-mat.quant-gas↗

arXiv2023

Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model

We characterize the equation of state (EoS) of the SU($N>2$) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for $N = 3, 4$ and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo (DQMC) and numerical linked cluster expansion (NLCE). By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU($N$) FHM.

cond-mat.quant-gas↗

arXiv2023

Charge order in the kagome lattice Holstein model: A hybrid Monte Carlo study

The Holstein model is a paradigmatic description of the electron-phonon interaction, in which electrons couple to local dispersionless phonon modes, independent of momentum. The model has been shown to host a variety of ordered ground states such as charge density wave (CDW) order and superconductivity on several geometries, including the square, honeycomb, and Lieb lattices. In this work, we study CDW formation in the Holstein model on the kagome lattice, using a recently developed hybrid Monte Carlo simulation method. We present evidence for $\sqrt{3} \times \sqrt{3}$ CDW order at an average electron filling of $\langle n \rangle =2/3$ per site, with an ordering wavevector at the $K$-points of the Brillouin zone. We estimate a phase transition occurring at $T_{c}\approx t/18$, where $t$ is the nearest-neighbor hopping parameter. Our simulations find no signature of CDW order at other electron fillings or ordering momenta for temperatures $T \geq t/20$.

cond-mat.str-el↗

arXiv2023

Universality and Critical Exponents of the Fermion Sign Problem

Initial characterizations of the fermion sign problem focused on its evolution with spatial lattice size $L$ and inverse temperature $β$, emphasizing the implications of the exponential nature of the decay of the average sign $\langle {\cal S} \rangle$ for the complexity of its solution and associated limitations of quantum Monte Carlo studies of strongly correlated materials. Early interest was also on the evolution of $\langle {\cal S} \rangle$ with density $ρ$, either because commensurate filling is often associated with special symmetries for which the sign problem is absent or because particular fillings are often primary targets, e.g.~those densities which maximize superconducting transition temperature (the top of the `dome' of cuprate systems). Here we describe a new analysis of the sign problem, which demonstrates that the {\it spin-resolved} sign $\langle {\cal S}_σ\rangle$ already possesses signatures of universal behavior traditionally associated with order parameters, even in the absence of symmetry protection that makes $\langle {\cal S} \rangle = 1$. When appropriately scaled, $\langle {\cal S}_σ\rangle$ exhibits universal crossings and data collapse. Moreover, we show these behaviors occur in the vicinity of quantum critical points of three well-understood models, exhibiting either second-order or Kosterlitz-Thouless phase transitions. Our results pave the way for using the average sign as a minimal correlator that can potentially describe quantum criticality in a variety of fermionic many-body problems.

cond-mat.str-el↗

arXiv2023

Magnetic and singlet phases in the three-dimensional periodic Anderson Model

Heavy fermion materials are compounds in which localized $f$-orbitals hybridize with delocalized $d$ ones, leading to quasiparticles with large renormalized masses. The presence of strongly correlated $f$-electrons at the Fermi level may also lead to long-range order, such as magnetism, or unconventional superconductivity. From a theoretical point of view, the ``standard model'' for heavy fermion compounds is the Periodic Anderson Model (PAM). Despite being extensively scrutinized, its thermodynamic properties in three-dimensional lattices have not been carefully addressed by unbiased methodologies. Here we investigate the 3D PAM employing state-of-the-art finite temperature auxiliary field quantum Monte Carlo simulations. We present the behavior of the kinetic energy, the entropy, the specific heat, and the double occupancy as functions of the temperature and the hybridization strength. From these quantities, and by the analysis of the spin-spin correlation functions, we investigate the occurrence of magnetic phase transitions at finite temperatures, and determine the phase diagram of the model, including the behavior of the Néel temperature as a function of the external parameters.

cond-mat.str-el↗

arXiv2022

Bilayer Hubbard model: Analysis based on the fermionic sign problem

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its `phase diagram' in the interplane hopping $t_\perp$ versus on-site interaction $U$ parameter space, at half filling, are largely in disagreement. Here we provide an analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small $U$. Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band insulator not yet explored in a variety of existing, unbiased numerical methods. Our work demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.

cond-mat.str-el↗

arXiv2022

Charge Singlets and Orbital-Selective Charge Density Wave Transitions

The possibility of "orbitally selective Mott transitions" within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion $U_1$ is insulating and another orbital, to which it is hybridized, with small $U_{-1}$, is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the co-existence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling (EPC). To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a "Holstein-Metal interface" where the electron-phonon coupling, $λ$, is zero in the "metallic" layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization $t_3$, but decreases and eventually vanishes as $t_3$ grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at intermediate ratio of inter- to intra-layer hopping strengths, $1.4 \lesssim t_3/t \lesssim 3.4$. This is consistent with the occurrence of an "orbitally selective CDW" regime at weak $t_3$ in which the layer with $λ_{1} \neq 0$ exhibits long-range charge order, but the "metallic layer" with $λ_{-1}=0$, to which it is hybridized, does not.

cond-mat.str-el↗

arXiv2022

Photoinduced enhancement of superconductivity in the plaquette Hubbard model

Real-time dynamics techniques have proven increasingly useful in understanding strongly correlated systems both theoretically and experimentally. By employing unbiased time-resolved exact diagonalization, we study pump dynamics in the two-dimensional plaquette Hubbard model, where distinct hopping integrals $t_h$ and $t_h^\prime$ are present within and between plaquettes. In the intermediate coupling regime, a significant enhancement of $d$-wave superconductivity is observed and compared with that obtained by simple examination of expectation values with the eigenstates of the Hamiltonian. Our work provides further understanding of superconductivity in the Hubbard model, extends the description of the pairing amplitude to the frequency-anisotropy plane, and offers a promising approach for experimentally engineering emergent out-of-equilibrium states.

cond-mat.str-el↗

arXiv2022

Effect of Emitters on Quantum State Transfer in Coupled Cavity Arrays

Over the last decade, conditions for perfect state transfer in quantum spin chains have been discovered, and their experimental realizations addressed. In this paper, we consider an extension of such studies to quantum state transfer in a coupled cavity array including the effects of atoms in the cavities which can absorb and emit photons as they propagate down the array. Our model is equivalent to previously examined spin chains in the one-excitation sector and in the absence of emitters. We introduce a Monte Carlo approach to the inverse eigenvalue problem which allows the determination of the inter-cavity and cavity-emitter couplings resulting in near-perfect quantum state transfer fidelity, and examine the time dependent polariton wave function through exact diagonalization of the resulting Tavis-Cummings-Hubbard Hamiltonian. The effect of inhomogeneous emitter locations is also evaluated.

quant-ph↗

arXiv2021

Hamming Distance and the onset of quantum criticality

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior. Here, utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, we suggest a significant advance on these ideas to extract the location of quantum critical points in various fermionic models, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. Our approach charts a path to circumvent inherent limitations imposed by the SP, allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via quantum Monte Carlo simulations.

cond-mat.str-el↗

arXiv2021

Universal thermodynamics of an SU($N$) Fermi-Hubbard Model

The SU(2) symmetric Fermi-Hubbard model (FHM) plays an essential role in strongly correlated fermionic many-body systems. In the one particle per site and strongly interacting limit ${U/t \gg 1}$, it is effectively described by the Heisenberg Hamiltonian. In this limit, enlarging the spin and extending the typical SU(2) symmetry to SU($N$) has been predicted to give exotic phases of matter in the ground state, with a complicated dependence on $N$. This raises the question of what -- if any -- are the finite-temperature signatures of these phases, especially in the currently experimentally relevant regime near or above the superexchange energy. We explore this question for thermodynamic observables by numerically calculating the thermodynamics of the SU($N$) FHM in the two-dimensional square lattice near densities of one particle per site, using determinant Quantum Monte Carlo and Numerical Linked Cluster Expansion. Interestingly, we find that for temperatures above the superexchange energy, where the correlation length is short, the energy, number of on-site pairs, and kinetic energy are universal functions of $N$. Although the physics in the regime studied is well beyond what can be captured by low-order high-temperature series, we show that an analytic description of the scaling is possible in terms of only one- and two-site calculations.

cond-mat.quant-gas↗

arXiv2021

Quantum Critical Points and the Sign Problem

The "sign problem" (SP) is the fundamental limitation to simulations of strongly correlated materials in condensed matter physics, solving quantum chromodynamics at finite baryon density, and computational studies of nuclear matter. As a result, it is part of the reason fields such as ultra-cold atomic physics are so exciting: they can provide quantum emulators of models that could not otherwise be solved, due to the SP. For the same reason, it is also one of the primary motivations behind quantum computation. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians, since the details of how it onsets, and its eventual occurrence, can be altered by the choice of algorithm or many-particle basis. Despite that, we show that the SP in determinant quantum Monte Carlo (DQMC) is quantitatively linked to quantum critical behavior. We demonstrate this via simulations of a number of fundamental models of condensed matter physics, including the spinful and spinless Hubbard Hamiltonians on a honeycomb lattice and the ionic Hubbard Hamiltonian, all of whose critical properties are relatively well understood. We then propose a reinterpretation of the low average sign for the Hubbard model on the square lattice when away from half-filling, an important open problem in condensed matter physics, in terms of the onset of pseudogap behavior and exotic superconductivity. Our study charts a path for exploiting the average sign in QMC simulations to understand quantum critical behavior, rather than solely as an obstacle that prevents quantum simulations of many-body Hamiltonians at low temperature.

cond-mat.str-el↗

arXiv2021

Magnetic properties of alternating Hubbard ladders

We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin densities as well as their correlation functions at half-filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries. Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.

cond-mat.str-el↗

arXiv2021

Charge Density Wave and Superconductivity in the Disordered Holstein Model

The interplay between electron-electron correlations and disorder has been a central theme of condensed matter physics over the last several decades, with particular interest in the possibility that interactions might cause delocalization of an Anderson insulator into a metallic state, and the disrupting effects of randomness on magnetic order and the Mott phase. Here we extend this physics to explore electron-phonon interactions and show, via exact quantum Monte Carlo simulations, that the suppression of the charge density wave correlations in the half-filled Holstein model by disorder can stabilize a superconducting phase. Our simulations thus capture qualitatively the suppression of charge ordered phases and emergent superconductivity recently seen experimentally.

cond-mat.str-el↗

arXiv2021

Electron-Phonon Interactions in Flat Band Systems

Existing Quantum Monte Carlo studies have investigated the properties of fermions on a Lieb (CuO$_2$) lattice interacting with an on-site, or near-neighbor electron-electron coupling. Attention has focused on the interplay of such interactions with the macroscopic degeneracy of local zero energy modes, from which Bloch states can be formed to produce a flat band in which energy is independent of momentum. The resulting high density of states, in combination with the Stoner criterion, suggests that there should be pronounced instabilities to ordered phases. Indeed, a theorem by Lieb rigorously establishes the existence of ferrimagnetic order. Here we study the charge density wave phases induced by electron-phonon coupling on the Lieb lattice, as opposed to previous work on electron-electron interactions. Our key result is the demonstration of charge density wave (CDW) phases at one-third and two-thirds fillings, characterized by long-range density density correlations between doubly occupied sites on the minority or majority sublattice, and an accompanying gap. We also compute the transition temperature to the ordered phase as a function of the electron-phonon coupling.

cond-mat.str-el↗

arXiv2020

Visualizing Strange Metallic Correlations in the 2D Fermi-Hubbard Model with AI

Strongly correlated phases of matter are often described in terms of straightforward electronic patterns. This has so far been the basis for studying the Fermi-Hubbard model realized with ultracold atoms. Here, we show that artificial intelligence (AI) can provide an unbiased alternative to this paradigm for phases with subtle, or even unknown, patterns. Long- and short-range spin correlations spontaneously emerge in filters of a convolutional neural network trained on snapshots of single atomic species. In the less well-understood strange metallic phase of the model, we find that a more complex network trained on snapshots of local moments produces an effective order parameter for the non-Fermi-liquid behavior. Our technique can be employed to characterize correlations unique to other phases with no obvious order parameters or signatures in projective measurements, and has implications for science discovery through AI beyond strongly correlated systems.

cond-mat.str-el↗