arXiv subjects

G. G. Batrouni

Publications and source records attributed to G. G. Batrouni.

At least 19 recordsLinked to original sources

arXiv2024

Field-induced Peierls phase in $S=1$ Heisenberg spins coupled to quantum phonons

Spin-Peierls transition occurs in a one-dimensional $S=1$ Heisenberg antiferromagnetic model with single-ion anisotropy, coupled to finite frequency bond phonons, in a magnetic field. Our results indicate that for the pure Heisenberg model, any Peierls transition is suppressed by quantum fluctuations of the phonon field. However, a novel magnetic field-induced Spin-Peierls phase is realized in the presence of strong single-ion anisotropy. Contrary to the standard Peierls state, the periodicity of bond strength modulation in this field-induced Spin-Peierls state is variable and depends on the strength of the applied field. The nature of the ground state in this new phase and the associated field-driven transitions to and out of this phase are explored using extensive numerical simulations. In particular, we explore the spin and bond correlations and the evolution of bond order modulation with varying magnetic field.

cond-mat.str-el↗

arXiv2024

Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model

Most nonperturbative numerical studies of electron-phonon interactions focus on model Hamiltonians where the electrons interact with a phonon branch via a single type of microscopic mechanism. Two commonly explored couplings in this context are the Holstein and Su-Schrieffer-Heeger (SSH) interactions, which describe phonons modulating the on-site energy and intersite electron hopping, respectively. Many materials, however, have multiple phonon branches that can each interact with electronic degrees of freedom in different ways. We present here a determinant quantum Monte Carlo study of the half-filled two-dimensional (bond) SSH-Holstein Hamiltonian, where electrons couple to different phonon branches via either the Holstein or SSH mechanism. We map the model's phase diagram and determine the nature of the transitions between charge-density wave, bond order wave, and antiferromagnetic order.

cond-mat.str-el↗

arXiv2023

Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential

The Holstein Hamiltonian describes itinerant electrons whose site density couples to local phonon degrees of freedom. In the single site limit, at half-filling, the electron-phonon coupling results in a double well structure for the lattice displacement, favoring empty or doubly occupied sites. In two dimensions, and on a bipartite lattice in $d \geq 2$, an intersite hopping causes these doubly occupied and empty sites to alternate in a charge density wave (CDW) pattern when the temperature is lowered. Because a discrete symmetry is broken, this occurs in a conventional second-order transition at finite $T_{\rm cdw}$. In this paper, we investigate the effect of changing the phonon potential energy to one with an intrinsic double well structure even in the absence of an electron-phonon coupling. While this aids in the initial process of pair formation, the implications for subsequent CDW order are non-trivial. One expects that, when the electron-phonon coupling is too strong, the double wells become deep and the polaron mass large, an effect which reduces $T_{\rm cdw}$. We show here the existence of regions of parameter space where the double well potential, while aiding local pair formation, does so in a way which also substantially enhances long range CDW order.

cond-mat.str-el↗

arXiv2022

Designer Flat Bands: Topology and Enhancement of Superconductivity

We construct quasi one-dimensional topological and non-topological three-band lattices with tunable band gap and winding number of the flat band. Using mean field (MF) and exact density matrix renormalization group (DMRG) calculations, we show explicitly how the band gap affects pairing and superconductivity (SC) in a Hubbard model with attractive interactions. We show excellent agreement between MF and DMRG. When a phase twist is applied on the system, a phase difference appears between pairing order parameters on different sublattices, and this plays a very important role in the SC density. The SC weight, $D_s$, on the gapped topological, $W\neq0$, flat band increases linearly with interaction strength, $U$, for low values, and with a slope that depends on the details of the compact localized state at $U=0$. As $U\to 0$ for the gapped non-topological flat band ($W=0$), $D_s$ decays with a power law faster than quadratic but slower than exponential. This indicates that isolated non-topological flat bands are less beneficial to SC. In the gapless case (flat band touching the band above it), we find at low $U$ (both for $W=0$ and $W\neq 0$) that $D_s\propto U^φ$ with $φ<1$ contrary to the $U{\rm ln}\, ({\rm const.}/U)$ behavior reported in the literature. In other words, $D_s$ increases faster than linearly for low $U$ thus favoring SC at weak interaction more than the gapped case. For systems with touching bands, we observe that the one-body correlation length, $ξ$, diverges as a power law as $U\rightarrow0$, while for the isolated flat band $ξ(U\to 0)$ is a constant smaller than one lattice spacing. Both behaviors are distinct from the exponential divergence of $ξ$ in the dispersive case. Our results re-establish that the BCS mean field and quantum metric alone are insufficient to characterize SC at weak coupling.

cond-mat.supr-con↗

arXiv2021

Pairing and superconductivity in quasi one-dimensional flat band systems: Creutz and sawtooth lattices

We study the pairing and superconducting properties of the attractive Hubbard model in two quasi one-dimensional topological lattices: the Creutz and sawtooth lattices. They share two peculiar properties: each of their band structures exhibits a flat band with a non-trivial winding number. The difference, however, is that only the Creutz lattice is genuinely topological, owing to a chiral (sub-lattice) symmetry, resulting in a quantized winding number and zero energy edge modes for open boundary conditions. We use mean field and exact density matrix renormalization group in our work. Our three main results are: (a) For both lattice systems, the superconducting weight, $D_s$, is linear in the coupling strength, $U$, for low values of $U$; (b) for small $U$, $D_s$ is proportional to the quantum metric for the Creutz system but not for the sawtooth system because its sublattices are not equivalent; (c) conventional BCS mean field is not appropriate for such systems with inequivalent sublattices. We show that, for a wide range of densities and coupling strengths, these systems are very well described by a full multi-band mean field method where the pairing parameters and the local particle densities on the inequivalent sublattices are variational mean field parameters.

cond-mat.supr-con↗

arXiv2021

Quantum Monte Carlo study of an anharmonic Holstein model

We study the effects of anharmonicity on the physics of the Holstein model, which describes the coupling of itinerant fermions and localized quantum phonons, by introducing a quartic term in the phonon potential energy. We find that the presence of this anharmonic term reduces the extent of the charge density wave phase (CDW) at half-filling as well as the transition temperature to this phase. Doping away from half-filling, we observe a first order phase transition between the CDW and a homogeneous phase which is also present in the harmonic model. In addition, we study the evolution of the superconducting susceptibility in the doped region and show that anharmonicity can enhance the superconducting response.

cond-mat.str-el↗

arXiv2020

Pairing and pair superfluid density in one-dimensional Hubbard models

We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity, there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e. Bardeen-Cooper-Schrieffer (BCS) pairing requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.

cond-mat.quant-gas↗

arXiv2020

Nonlinear two-photon Rabi-Hubbard model: superradiance and photon/photon-pair Bose-Einstein condensate

We study the ground state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo (QMC) simulations and density matrix renormalization group (DMRG) calculations. Our model includes a nonlinear photon-photon interaction term. Absent this term, the RH model has only one phase, the normal disordered phase, and suffers from spectral collapse at larger values of the photon-qubit interaction or inter-cavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system which now exhibits {\it two} quantum phase transitions: Normal phase to {\it photon pair} superfluid (PSF) transition and PSF to single particle superfluid (SPSF). The discrete $Z_4$ symmetry of the Hamiltonian spontaneously breaks in two stages: First it breaks partially as the system enters the PSF and then completely breaks when the system finally enters the SPSF phase. We show detailed numerical results supporting this, and map out the ground state phase diagram.

cond-mat.quant-gas↗

arXiv2020

Langevin Simulations of the Half-Filled Cubic Holstein Model

Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature $T_{cdw}$ of the half-filled two dimensional Holstein model in square and honeycomb lattices have become available for the first time. Exploiting the further development of numerical methodology, here we present results in three dimensions, which are made possible through the use of Langevin evolution of the quantum phonon degrees of freedom. In addition to determining $T_{cdw}$ from the scaling of the charge correlations, we also examine the nature of charge order at general wave vectors for different temperatures, couplings, and phonon frequencies, and the behavior of the spectral function and specific heat.

cond-mat.str-el↗

arXiv2019

Dominant charge-density-wave correlations in the Holstein model on the half-filled square lattice

We use an unbiased, continuous-time quantum Monte Carlo method to address the possibility of a zero-temperature phase without charge-density-wave (CDW) order in the Holstein and, by extension, the Holstein-Hubbard model on the half-filled square lattice. In particular, we present results spanning the whole range of phonon frequencies, allowing us to use the well understood adiabatic and antiadiabatic limits as reference points. For all parameters considered, our data suggest that CDW correlations are stronger than pairing correlations even at very low temperatures. These findings are compatible with a CDW ground state that is also suggested by theoretical arguments.

cond-mat.str-el↗

arXiv2019

Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: photon pair superradiance, Mott insulator and normal phases

We study the ground state phase diagrams of two-photon Dicke, the one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean field, perturbation, quantum Monte Carlo (QMC), and density matrix renormalization group (DMRG) methods. We first compare mean field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also unlike the one-photon case, the SF phases above and below the Mott are surprisingly different: Below the Mott, the SF is that of photon {\it pairs} as opposed to above the Mott where it is SF of simple photons. The mean field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.

cond-mat.other↗

arXiv2019

Charge Order in the Holstein Model on a Honeycomb Lattice

The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin liquid phase between the semi-metal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo (DQMC) to study the Holstein model on a Honeycomb lattice and explore the role of electron-phonon interactions on Dirac fermions. We show that they give rise to charge density wave (CDW) order, and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.

cond-mat.str-el↗

arXiv2019

One-dimensional Hubbard-Holstein model with finite range electron-phonon coupling

The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling $g$ to the phonons drives the system towards a Peierls charge density wave state whereas increasing the electron-electron interaction $U$ drives the fermions into a Mott antiferromagnet. At low $g$ and $U$, or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with characteristic range $ξ$, interpolating between the Holstein and Fröhlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $ξ$, and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction $U$ will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U \ne 0$ case, even for small values of the coupling range.

cond-mat.str-el↗

arXiv2018

Langevin Simulations of a Long Range Electron Phonon Model

We present a Quantum Monte Carlo (QMC) study, based on the Langevin equation, of a Hamiltonian describing electrons coupled to phonon degrees of freedom. The bosonic part of the action helps control the variation of the field in imaginary time. As a consequence, the iterative conjugate gradient solution of the fermionic action, which depends on the boson coordinates, converges more rapidly than in the case of electron-electron interactions, such as the Hubbard Hamiltonian. Fourier Acceleration is shown to be a crucial ingredient in reducing the equilibration and autocorrelation times. After describing and benchmarking the method, we present results for the phase diagram focusing on the range of the electron-phonon interaction. We delineate the regions of charge density wave formation from those in which the fermion density is inhomogeneous, caused by phase separation. We show that the Langevin approach is more efficient than the Determinant QMC method for lattice sizes $N \gtrsim 8 \times 8$ and that it therefore opens a potential path to problems including, for example, charge order in the 3D Holstein model.

cond-mat.str-el↗

arXiv2017

Phonon dispersion and the competition between pairing and charge order

The Holstein Model (HM) describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits, but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature $T_{\rm cdw}$ for CDW order, and also uncover several novel features of diagonal long range order in the phase diagram, including a competition between charge patterns at momenta ${\bf q}=(π,π)$ and ${\bf q}=(0,π)$ which lends insight into the relationship between Fermi surface nesting and the wavevector at which charge order occurs. We also demonstrate SC order at half-filling in situations where nonzero bandwidth sufficiently suppresses $T_{\rm cdw}$.

cond-mat.str-el↗

arXiv2017

Phase Diagram of Bosons in a 2D Optical Lattice with infinite-range Cavity-mediated Interactions

High-finesse optical cavity allows the establishment of long-range interactions between bosons in an optical lattice when most cold atoms experiments are restricted to short-range interactions. Supersolid phases have recently been experimentally observed in such systems. Using both exact quantum Monte Carlo simulations and Gutzwiller approximation, we study the ground state phase diagrams of a two-dimensional Bose-Hubbard model with infinite-range interactions which describes such experiments. In addition to superfluid and insulating Mott phases, the infinite-range checkerboard interactions introduce charge density waves and supersolid phases. We study here the system at various particle densities, elucidate the nature of the phases and quantum phase transitions, and discuss the stability of the phases with respect to phase separation. In particular we confirm the existence and stability of a supersolid phase detected experimentally.

cond-mat.quant-gas↗

arXiv2016

Quantum Monte Carlo Study of the Rabi-Hubbard Model

We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of a one dimensional Rabi-Hubbard model. The model consists of a lattice of Rabi systems coupled by a photon hopping term between near neighbor sites. For large enough coupling between photons and atoms, the phase diagram generally consists of only two phases: a coherent phase and a compressible incoherent one separated by a quantum phase transition (QPT). We show that, as one goes deeper in the coherent phase, the system becomes unstable exhibiting a divergence of the number of photons. The Mott phases which are present in the Jaynes-Cummings-Hubbard model are not observed in these cases due to the presence of non-negligible counter-rotating terms. We show that these two models become equivalent only when the detuning is negative and large enough, or if the counter-rotating terms are small enough.

cond-mat.other↗

arXiv2015

Bosonic Kondo-Hubbard model

We study, using quantum Monte-Carlo simulations, the bosonic Kondo-Hubbard model in a two dimensional square lattice. We explore the phase diagram and analyse the mobility of particles and magnetic properties. At unit filling, the transition from a paramagnetic Mott insulator to a ferromagnetic superfluid appears continuous, contrary to what was predicted with mean field. For double occupation per site, both the Mott insulating and superfluid phases are ferromagnetic and the transition is still continuous. Multiband tight binding Hamiltonians can be realized in optical lattice experiments, which offer not only the possibility of tuning the different energy scales over wide ranges, but also the option of loading the system with either fermionic or bosonic atoms.

cond-mat.quant-gas↗