arXiv subjects

Garry Goldstein

Publications and source records attributed to Garry Goldstein.

At least 37 records · Page 2Linked to original sources

arXiv2024

Higher Derivative Muffin Tin Orbitals (HDMTO) and Higher Derivative Koringa Khon and Rostoker (HDKKR) methods

In this work we introduce a Linearized version of the Koringa Khon and Rostoker method (LKKR) and show it to be equivalent to the Linearized Muffin Tin Orbitals method (LMTO). We then present higher derivative versions of both methods, e.g. HDKKR and HDMTO and show them to be partially distinct (not equivalent). In particular HDKKR basis set does not have an equivalent ground state for the Khon Sham (KS) Hamiltonian as the HDKKR basis set and has greater variational power than the HDMTO one. Because the KS method, for Density Functional Theory (DFT), is variational HDKKR will give better ground state energies than HDMTO. However HDKKR is much harder to work with then HDMTO requiring much greater computer resources so HDMTO can often be preferred.

physics.chem-ph↗

arXiv2022

Logical Majorana zero modes in a nanowire network

We present a scheme to use physical Majorana quasi-zero modes at each junction of a two-dimensional nanowire network to build a logical Majorana zero mode, the location of which is controllable through gate voltages. The wire-network is a way to realize a proposal by Yang et al. arXiv:1808.04825 to imprint a Kekulé vortex pattern on a honeycomb lattice via gate voltages. We show that a specific type of junction -- other than a naive Y- or T-junction -- is needed to realize, without breaking time-reversal symmetry, an artificial ``graphene'' system with Majorana fermions instead of complex ones at each site. The junction we propose (i) traps exactly one physical Majorana (quasi-)zero mode at each site of either a brick wall or honeycomb lattice and (ii) allows this mode to hybridize with all three neighboring sites. Using a lattice of these junctions and starting from an electronic, tight-binding model for the wires, we imprint the voltage patterns corresponding to the Kekulé vortex and observe the emergence of the logical Majorana zero mode at the vortex core. We also provide the range of parameters where this excitation could be realized experimentally.

cond-mat.mes-hall↗

arXiv2022

Lifetime of Excitations in Atomic and Molecular Bose-Einstein Condensates

Recent experimental progress has produced Molecular Superfluids (MSF) in thermal equilibrium; this opens the door to a new class of experiments investigating the associated thermodynamic and dynamical responses. We review the theoretical picture of the phase diagram and quasiparticle spectrum in the Atomic Superfluid (ASF) and MSF phases. We further compute the parametric dependence of the quasiparticle lifetimes at one-loop order. In the MSF phase, the $U(1)$ particle number symmetry breaks to $\mathbb{Z}_2$ and the spectrum exhibits a gapless Goldstone mode in addition to a gapped $\mathbb{Z}_2$-protected atom-like mode. In the ASF phase, the $U(1)$ symmetry breaks completely, leaving behind a Goldstone mode and an unprotected gapped mode. In both phases, the Goldstone mode decays with a rate given by the celebrated Belyaev result, as in a single component condensate. In the MSF phase, the gapped mode is sharp up to a critical Cherenkov momentum beyond which it emits phonons. In the ASF phase, the gapped mode decays with a constant rate even at small momenta. These decay rates govern the spectral response in microtrap tunneling experiments and lead to sharp features in the transmission spectrum of atoms fired through molecular clouds.

cond-mat.quant-gas↗

arXiv2022

Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions

Starting with general semiclassical equations of motion for electrons in the presence of electric and magnetic fields, we extend the Chambers formula to include in addition to a magnetic field, time-dependent electric fields and bands with Berry curvature. We thereby compute the conductivity tensor $σ_{αβ}(B,ω)$ in the presence of magnetic field for bands in two (2D) and three (3D) dimensions with Berry curvature. We focus then on several applications to magnetotransport for metals with Fermi surface topological transitions in 2D. In particular, we consider a rectangular lattice and a model related to overdoped graphene, to investigate the signatures of different types of Fermi surface topological transitions in metals in the Hall coefficient, Hall conductivity $σ_{xy}$ and longitudinal conductivity $σ_{xx}$. The behavior of those quantities as a function of frequency, when the electric field is time dependent, is also investigated. As an example of non-zero Berry curvature, we study the magnetotransport of the Haldane model within this context. In addition, we provide the linear and nonlinear electric current formula to order $E^2$.

cond-mat.mes-hall↗

arXiv2020

Extending the Gutzwiller approximation to intersite interactions

We develop an extension of the Gutzwiller Approximation (GA) formalism that includes the effects of Coulomb interactions of arbitrary range (including density density, exchange, pair hopping and Coulomb assisted hopping terms). This formalism reduces to the ordinary GA formalism for the multi-band Hubbard models in the presence of only local interactions. This is accomplished by combining the 1/z expansion -- where z is the coordination number and only the leading order terms contribute in the limit of infinite dimensions -- with a P^2-I expansion, where P is the Gutzwiller projector. The method is conveniently formulated in terms of a Gutzwiller Lagrange function. We apply our theory to the extended single band Hubbard model. Similarly to the usual Brinkman-Rice mechanism we find a Mott transition. A valence skipping transition is observed, where the occupation of the empty and doubly occupied states for the Gutzwiller wavefunction is enhanced with respect to the uncorrelated Slater determinant wavefunction.

cond-mat.str-el↗

arXiv2019

Generalised route to effective field theories for quantum systems with local constraints

Some of the exciting phenomena uncovered in strongly correlated systems in recent years - for instance quantum topological order, deconfined quantum criticality, and emergent gauge symmetries -- appear in systems in which the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedom. Cases in point include spin liquids, valence bond systems, dimer models, and vertex models. In this work, we use a slave boson description coupled to a large-$S$ path integral formulation to devise a generalised route to obtain effective field theories for such systems. We demonstrate the validity and capability of our approach by studying quantum dimer models and by comparing our results with the existing literature. Field-theoretic approaches to date are limited to bipartite lattices, they depend on a gauge-symmetric understanding of the constraint, and they lack generic quantitative predictive power for the coefficients of the terms that appear in the Lagrangians of these systems. Our method overcomes all these shortcomings and we show how the results up to quadratic order compare with the known height description of the square lattice quantum dimer model, as well as with the numerical estimate of the speed of light of the photon excitations on the diamond lattice. Finally, instanton considerations allow us to infer properties of the finite-temperature behaviour in two dimensions.

cond-mat.str-el↗

arXiv2019

Quantum oscillations and criticality in a fermionic and bosonic dimer model for the cuprates

We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. Based on gauge invariance, we argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the d-wave superconducting pairing amplitude when anti-ferromagnetic interactions are included. Our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.

cond-mat.str-el↗

arXiv2018

Steady-state superconductivity in electronic materials with repulsive interactions

We study the effect of laser driving on a minimal model for a hexagonal two-dimensional material with broken inversion symmetry. Through the application of circularly polarised light and coupling to a thermal free electron bath, the system is driven into a nonequilibrium steady state with asymmetric, nonthermal carrier populations in the two valleys. We show that, in this steady state, interband superconducting correlations between electrons can develop independent of the sign of the electron-electron interactions. We discuss how our results apply, for example, to transition metal dichalcogenides. This work opens the door to technological applications of superconductivity in a range of materials that were hitherto precluded from it.

cond-mat.str-el↗

arXiv2018

Hall coefficient and magnetoresistance in boson+fermion dimer models for the pseudogap phase of high Tc superconductors

We show that the Hall coefficient of the boson+fermion dimer model for the pseudogap phase of high temperature superconductivity introduced in Punk et al. changes sign from negative at low temperatures to positive at high temperatures at a characteristic temperature scaling proportional to the the cyclotron frequency of the fermionic dimers (divided by k), (here k~0.7 fits the experimental data well). We show that this is an effect of the changing of the sign of the coupling between the fermionic dimer and the magnetic field from negative coupling -e at low temperatures to positive coupling +e at high temperature, with the Hall coefficient being proportional to R_H~e_B*e_E*e_J (the product of the magnetic charge, electric charge and current charge all of which we carefully define). We relate the Hall conductivity to the coefficient in Kohler's like rule for magnetoconductivity and calculate some corrections which are relevant near the intermediate temperature range ~50K (typical values for the cyclotron frequency of the dimers). Furthermore we make a sharp prediction that the magnetoresistance effect vanishes to order B^2 at the temperature and magnetic field where the Hall coefficient vanishes.

cond-mat.str-el↗

arXiv2016

Electrons at the monkey saddle: a multicritical Lifshitz point

We consider 2D interacting electrons at a monkey saddle with dispersion $\propto p_x^3-3p_xp_y^2$. Such a dispersion naturally arises at the multicritical Lifshitz point when three van Hove saddles merge in an elliptical umbilic elementary catastrophe, which we show can be realized in biased bilayer graphene. A multicritical Lifshitz point of this kind can be identified by its signature Landau level behavior $E_m\propto (Bm)^{3/2}$ and related oscillations in thermodynamic and transport properties, such as de Haas-van Alphen and Shubnikov-de Haas oscillations, whose period triples as the system crosses the singularity. We show, in the case of a single monkey saddle, that the non-interacting electron fixed point is unstable to interactions under the renormalization group flow, developing either a superconducting instability or non-Fermi liquid features. Biased bilayer graphene, where there are two non-nested monkey saddles at the $K$ and $K^\prime$ points, exhibits an interplay of competing many-body instabilities, namely s-wave superconductivity, ferromagnetism, and spin- and charge-density wave.

cond-mat.str-el↗

arXiv2016

D-wave superconductivity in boson+fermion dimer models

We present a slave-particle mean-field study of the mixed boson+fermion quantum dimer model introduced by Punk, Allais, and Sachdev [PNAS 112, 9552 (2015)] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge e fermion pockets whose total area is equal to the hole doping p, for a range of parameters consistent with the t-J model for high temperature superconductivity. Here we find that the dimers are unstable to d-wave superconductivity at low temperatures. The region of the phase diagram with d-wave rather than s-wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone.

cond-mat.str-el↗

arXiv2016

Band-edge superconductivity

We show that superconductivity can arise in semiconductors with a band in the shape of a Mexican hat when the chemical potential is tuned close to the band edge, but not intersecting the band, as long as interactions are sufficiently strong. Hence, this is an example where superconductivity can emerge from a band insulator when interactions exceed a threshold. Semiconductors with simple cubic symmetry point groups and with strong spin-orbit coupling provide an example of a system with such band dispersion.

cond-mat.supr-con↗

arXiv2016

Failure of the GGE hypothesis for integrable models with bound states

In this work we study the applicability of the GGE to integrable one dimensional systems with bound states. We find that the GGE fails to describe the long time dynamics for most initial states including eigenstates. We present our calculations studying the attractive Lieb-Liniger gas and the XXZ magnet, though similar results may be obtained for other models.

cond-mat.quant-gas↗

arXiv2015

Correlation functions of the Lieb-Liniger gas and the LeClair-Mussardo formula

In this letter we derive formulas for multi point correlation functions, in the thermodynamic limit, for the Lieb Liniger gas taken with respect to arbitrary eigenstates. These results apply for the ground state, thermal states and GGE states. We obtain these correlation functions as a series of multiple integrals of progressively higher dimensions. These integrals converge rapidly for short distance correlation functions and low densities of particles. The series derived matches exactly the LeClair Mussardo formula for correlation functions of relativistic integrable models.

cond-mat.quant-gas↗

arXiv2015

Photo-induced superconductivity in semiconductors

We show that optically pumped semiconductors can exhibit superconductivity. We illustrate this phenomenon in the case of a two-band semiconductor tunnel-coupled to broad-band reservoirs and driven by a continuous wave laser. More realistically, we also show that superconductivity can be induced in a two-band semiconductor interacting with a broad-spectrum light source. We furthermore discuss the case of a three-band model in which the middle band replaces the broad-band reservoirs as the source of dissipation. In all three cases, we derive the simple conditions on the band structure, electron-electron interaction, and hybridization to the reservoirs that enable superconductivity. We compute the finite superconducting gap and argue that the mechanism can be induced through both attractive and repulsive interactions and is robust to high temperatures.

cond-mat.supr-con↗

arXiv2015

Equilibration and GGE for hard wall boundary conditions

In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the GGE formalism are applicable for the long time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton cradle experiment. We calculate the time average of various correlation functions for long times after the quench.

cond-mat.quant-gas↗

arXiv2015

Driven-dissipative ising model: mean field solution

We study the fate of the Ising model and its universal properties when driven by a rapid periodic drive and weakly coupled to a bath at equilibrium. The far from equilibrium steady-state regime of the system is accessed by means of a Floquet mean field approach. We show that, depending on the details of the bath, the drive can strongly renormalize the critical temperature to higher temperatures, modify the critical exponents, or even change the nature of the phase transition from second to first order after the emergence of a tricritical point. Moreover, by judiciously selecting the frequency of the field and by engineering the spectrum of the bath, one can drive a ferromagnetic Hamiltonian to an antiferromagnetically ordered phase and vice-versa.

cond-mat.stat-mech↗

arXiv2014

Stron eigenstate thermalization hypothesis

We present a generalization of the ETH conjecture. Using this generalization we are able to derive the fact that an arbitrary eigenstate of a general many body system may be used to represent microcanonical ensemble in any many body experiment that involves only local operators and projectors onto eigenstates of the system Hamiltonian. In particular we extend the ETH to include some non-local operators. We present a derivation of this conjecture in the case of a many body model whose Hamiltonian is composed of two parts: an integrable Hamiltonian and a small but finite Gaussian perturbation.

cond-mat.stat-mech↗