arXiv subjects

Garry Goldstein

Publications and source records attributed to Garry Goldstein.

At least 19 recordsLinked to original sources

arXiv2026

Inhomogeneous Coulomb Models Without Defects are Sick: Domain Wall Energies Scaling as Volume (not Boundary Area)

In this work we show that coulomb models, ones that obey a $\nabla\cdot\left\langle \mathbf{B}\right\rangle =0$ divergence free constraint - for $\left\langle \mathbf{B}\right\rangle $ being some coarse grained variables related to the microscopic degrees of freedom of the lattice system - are sick without the inclusion of defects with $\nabla\cdot\mathbf{B}\neq0$. We show that for generic boundaries (ones where the fluxes of the pseudo-magnetic fields on the boundary do not cancel: $\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}\neq0$ - here $\mathbf{n}$ is the unit normal and $\left\langle \mathbf{B}_{R/L}\right\rangle $ are the two ground state pseudo-magnetic fields on either side of the domain wall) without the inclusion of defects, sharp domain walls (on the order of the width of a unit cell) between different phases of the system cost energy proportional to system size (not boundary area). We present several different examples of this phenomena in the square lattice six vertex model, in quantum dimers and in classical spin ice in the presence of magnetic fields. We also show by example that the condition $\left(\left\langle \mathbf{B}_{R}\right\rangle -\left\langle \mathbf{B}_{L}\right\rangle \right)\cdot\mathbf{n}=0$ is a necessary but not sufficient condition for the boundaries to be compatible - that is domain wall energy to scale with domain wall area and not system size. To further present the importance of boundary conditions in Coulomb systems we show that system boundaries, even ones that satisfy $\int_{\partial V}\mathbf{B}\cdot\mathbf{n}=0$, have thermodynamic consequences - that is there is a cost, extensive in system size, to the Helmholtz free energy.

cond-mat.str-el↗

arXiv2026

Failure of the Quench Action Formalism for Mott Insulator Initial States

The quench action formalism relies on the assumption that the overlap between a generic initial state $\left|\Psi_{0}\right\rangle $ and an eigenstate of an integrable model - defined through the rapidities $\left|k_{1},...k_{N}\right\rangle $ - can be written as: \begin{equation} \left\langle k_{1},...k_{N}\mid\Psi_{0}\right\rangle =\exp\left(-S_{\Psi_{0}}\left(\rho\left(k\right)\right)\right),\label{eq:Exponential} \end{equation} where $\rho\left(k\right)$ is the quasiparticle density of the state $\left|k_{1},...k_{N}\right\rangle $ and $S_{\Psi_{0}}$ is some smooth function of $\rho\left(k\right)$ that depends on $\Psi_{0}$. In particular the quench action formalism assumes the overlap depends smoothly on the quasiparticle density $\rho\left(k\right)$. In this work, by explicit counter example, we show that this is not the case. We consider the quench between a Mott insulator and a Lieb Liniger gas. We show that the overlap between the ground state of the Mott insulator and arbitrary eigenstates of the Lieb Liniger gas has a highly singular behavior and no expression like Eq. (1) applies. We do so within the Tonks Girardeau limit of the Lieb Liniger gas and to leading order in the $1/c$ expansion for the overlap (with $c$ being the coupling constant of the Lieb Liniger gas). In the Appendix we show similar results for overlaps in the XXZ model with crystal states.

cond-mat.quant-gas↗

arXiv2025

A Systematic Convergent Sequence of Approximations (of Integral Equation Form) to the Solutions of the Hedin Equations

In many ways the solution to the Hedin equations represents an exact solution to the many body problem. However, for most systems of practical interest, the solution to the Hedin equations is rendered nearly numerically intractable because the Hedin equations are of functional derivative form. Integral equations, on the other hand, are much more numerically tractable, than functional derivative equations, as they can often be solved iteratively. In this work we present a systematic set of integral equations (with no functional derivatives) - Hedin approximations I, II, III, IV etc. - whose solutions converge to the solutions of the exact Hedin equations. The Hedin approximations are well suited to iterative numerical solutions (which we also describe). Furthermore Hedin approximation I is just the GW approximation (as such this work may be viewed as a systematic improvement of the GW approximation). We present a systematic study of the Hedin equations for zero dimensional field theory (which, in particular, is a method to enumerate Feynman diagrams for field theories in arbitrary dimensions) and show better and better convergence to the solutions of the Hedin equations for higher and higher Hedin approximations, with Hedin approximations I, II and III being explicitly studied. We, in particular, show that the higher Hedin approximations capture more and and more Feynman diagrams for the self energy. We also show that already Hedin approximation II captures more diagrams than the state of the art diagrammatic vertex corrections approach. Furthermore Hedin approximation III is a near perfect match to the exact solutions of the Hedin equations, at least in the zero dimensional case, and enumerates a large number of Feynman diagrams.

cond-mat.str-el↗

arXiv2025

Spin Squeezing of Macroscopic Nuclear Spin Ensembles

Spin squeezing has been explored in atomic systems as a tool for quantum sensing, improving experimental sensitivity beyond the spin standard quantum limit for certain measurements. To optimize absolute metrological sensitivity, it is beneficial to consider macroscopic spin ensembles, such as nuclear spins in solids and liquids. Coupling a macroscopic spin ensemble to a parametrically-modulated resonant circuit can create collective spin squeezing by generating spin correlations mediated by the circuit. We analyze the squeezing dynamics in the presence of decoherence and finite spin polarization, showing that achieving 7 dB spin squeezing is feasible in several nuclear spin systems. The metrological benefit of squeezing a macroscopic spin ensemble lies in the suppression of technical noise sources in the spin detection system relative to the spin projection noise. This expands the experimental sensitivity bandwidth when searching for signals of unknown frequency and can improve the resonant signal-to-noise ratio. Squeezing macroscopic spin ensembles may prove to be a useful technique for fundamental physics experiments aimed at detecting spin interactions with oscillating background fields, such as ultralight dark matter.

hep-ph↗

arXiv2024

Kondo Impurities at a Finite Concentration of Impurities

In this work we study the Kondo impurity problem - at a finite concentration of impurities. We identify two parameter regimes for the Kondo impurity problem. 1) The single impurity limit, where the concentration of Kondo impurities is so low that the background scattering mechanisms (non-magnetic impurities, Umklapp scattering, etc.) of the metal considered are the dominant conduction electron scattering mechanisms at zero temperature. 2) The dilute impurity system limit where the concentration of magnetic impurities is such that they form the dominant mechanism of conduction electron scattering at zero temperature of the metal in question (this is accompanied by a variety of easily detectable Kondo signatures (resistance minimum, specific heat measurements, magnetization as a function of external magnetic field, conduction electron dephasing rates as well as ARPES, RIXS and NMR spectroscopies)) while still being very dilute. Most theoretical efforts are currently in regime where a single isolated impurity is considered - regime 1) while most experimental efforts are in regime 2). We present analytical evidence that this explains the well known discrepancy between experiment and theory as to the value of the Kondo temperature. We find that the ratio between the two Kondo temperatures in regime 1) and regime 2) is given by: $\mathcal{R}=\exp\left[\frac{\pi^{2}\rho v_{F}}{2k_{F}^{2}Vol}\right]$ where $\rho$ is the density of states, $v_{F}$ is the fermi velocity, and $k_{F}$ is the Fermi wavevector and $Vol$ is the volume of a unit cell. We note that there is no dependence on the impurity concentration in this ratio so it is possible to define a single Kondo temperature for limit 2) for the dilute Kondo impurity system. In this work we present results within the Reed-Newns Kondo meanfield approximation and to leading order of the linked cluster expansion.

cond-mat.str-el↗

arXiv2024

Energy Window Muffin Tin Orbitals (EWMTO) and Energy Window Linear Muffin Tin orbitals (EWLMTO) within the Atomic Sphere Approximation (ASA)

In this work we propose two new, closely related, efficient basis sets for the electronic structure problem. The basis sets are based on the Muffin Tin Orbital (MTO) idea that the eigenstates of the Khon Sham (KS) Hamiltonian may we be expanded in terms of eigenstates of the spherically averaged KS Hamiltonian inside the so called Muffin Tin (MT) spheres and Bessel functions in the interstitial multiplied by appropriate spherical Harmonics. Here we use the fact that the solution to the finding the ground state electron density is most often found through an iterative process: where generically on the order of over twenty iterations are taken till the ground state electron density and energy converges to the lowest values allowed by the correlation and exchange functional. We use eigenstate information from the previous iteration loop to choose the energies of the basis set elements used to study the KS Hamiltonian. Furthermore within the Atomic Sphere Approximation (ASA) the energies of the Bessel functions do not matter, as they are cancelled out other than for boundary conditions, and are chosen at zero energy. This is an efficient method aimed at studying the electronic structure of materials with large unit cells especially if they are of close packed form where ASA is particularly accurate.

cond-mat.mtrl-sci↗

arXiv2024

Projected Augmented Waves (PAW): extended resolution of unity method

The Projected Augmented Waves (PAW) method is based on a linear transformation between the pseudo wavefunctions and the all electron wavefunctions. To obtain high accuracy with this method, it is important that the local part of the linear transform (inside each atomic sphere) be defined over a complete basis set (with deviations from completeness leading to corrections to the total energy not computed within current implementations of PAW). Here we show how to make this basis much closer to complete without significant additional computational work and without modifying the transformation in any significant way thereby making the modifications we propose easy to implement in current electronic structure codes for PAW.. This is done by extending the resolution of unity used for the transform to include more smooth wavefunctions (which have nothing to do with the atomic problem) and having them linearly transform via the identity.

cond-mat.other↗

arXiv2024

Energy Window Augmented Plane Waves Approach to Density Functional Theory

In this work we present a new method for basis set generation for electronic structure calculations of crystalline solids. This procedure is aimed at applications to Density Functional Theory (DFT). In this construction, Energy Window Augmented Plane Waves (EWAPW), we take advantage of the fact that most DFT calculations use a convergence loop in order to obtain the self consistent eigenstates of the final (converged) Kohn Sham (KS) Hamiltonian. Here we propose that, for the basis used at each step of the self consistency iteration, we use the previous eigenstate basis, in the interstitial region, and augment it, inside each Muffin Tin (MT) sphere, with the solution to the spherically averaged KS Hamiltonian for the linearization energy of the energy window which contains the energy of that previous eigenstate. Indeed, to reduce the number of times the spherically averaged KS potential needs to be solved inside the MT spheres it is advantageous break up the spectrum into non-overlapping intervals, windows, and solve the spherically averaged KS Hamiltonian inside the MT region only once per window per angular momentum channel (at the linearization energy relevant to that window, usually near the middle of the window). For practical applications it is reasonable to have on the order of five to fifty windows. At each step of the iteration of the solution of the KS equations the EWAPW basis is that of near eigenstates of the KS Hamiltonian for that iteration. Overall the basis size is the comparable with the Augmented Plane Waves (APW) basis set but the number of radial wavefunctions is comparable or greater to Linearized Augmented Plane Waves + Local Orbitals + Higher Derivative Local Orbitals + High Energy Local Orbitals (LAPW+LO+HDLO+HELO) basis set.

cond-mat.mtrl-sci↗

arXiv2024

Classical action for the height within the Kardar-Parisi-Zhang (KPZ) equation for surface growth

In this work we write down a classical (not quantum) action for the surface height for the Kardar-Parisi-Zhang (KPZ) equation for surface growth. We do so starting with the regular Martin-Siggia-Rose (MSR) action (which is quantum - contains the constraint field) and integrate out the quantum constraint field exactly. We analyze the classical action, we thereby obtain, within the gaussian and one loop approximations various instabilities to rough surfaces. The gaussian analysis predicts instabilities to rough surfaces below two dimensions while one loop analysis predicts stronger surface stability to roughness and instabilities to roughness below one dimension rather than two dimensions. The one loop analysis shows that the KPZ action is incomplete and that we generate additional terms (not found in the initial classical action) in the action perturbatively. In the supplement we also modify the KPZ equation for growing surfaces to include the effect of surface tilt on the noise (that is have two sources of noise one of which is multiplicatively coupled noise).

cond-mat.stat-mech↗

arXiv2024

The effect of Coulomb assisted hopping on STM signal: extended two site Hubbard model analysis

In this work we study STM signal in the presence of Coulomb assisted hopping. We perform an extended two site Hubbard model analysis between the atom on the tip and the atom in the sample nearest to each other. We show that in the presence of Coulomb assisted hopping the STM signal depends on several spectral functions thereby complicating its interpretation. Furthermore in the broadband tip limit there are now three different competing rates for the total current (instead of one for the usual two site Hubbard model analysis used in the literature so far). We find an exact (within the Fermi golden rule - that is in the limit of weak coupling between tip and sample) expression for the current as a function of the bias voltage. As an example we apply our calculations to the case of free fermions with a uniform density of states. Even in this simple case there are non-trivial corrections - where the $dI/d\mathcal{V}$ (the rate of change of the current with respect to bias voltage) is not uniform as a two site (non-extended) Hubbard model analysis would predict. We also show that for realistic conditions the corrections predicted here are order one.

cond-mat.str-el↗

arXiv2024

Time reversal invariant topological 1D and 2D superconductors: doubling the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Oppen proposals

In this work we present a doubled version of the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Open proposals thereby obtaining time reversal invariant p-wave superconductivity in both 1D and 2D. This construction is much like the Kane-Mele spin Hall model which is a time reversal invariant doubling of the Haldane model. We show that the low energy effective action for these doubled versions of the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Open models corresponds to a single band p-wave time reversal invariant superconductors with pseudo spin degree of freedom instead of spin degree of freedom. There are Majorana fermions at the ends of wires or in vortex cores of these superconductors. Furthermore these are shown to be stable to small perturbations. In the supplement we present physical realization of the system with cold atoms and show a related "no-go" theorem given in Haim et. al. (2019) has too restrictive assumptions to apply to this proposal.

cond-mat.str-el↗

arXiv2024

Four center integrals for Coulomb interactions in small molecules

In this work we make some progress on studying four center integrals for the Coulomb energy for both Hartree Fock (HF) and Density Functional Theory (DFT) calculations for small molecules. We consider basis wave functions of the form of an arbitrary radial wave function multiplied by a spherical harmonic and study four center Coulomb integrals for them. We reformulated these Coulomb four center integrals in terms of some derivatives of integrals of nearly factorable functions which then depend on the Bessel transform of the radial wave functions considered.

cond-mat.other↗

arXiv2024

Projected Augmented Waves (PAW) motivated mixed basis sets for small molecules

The success behind many pseudopotential methods, such as the Projected Augmented Waves (PAW) and the Phillips-Kleinman pseudopotential methods, is that these methods are nearly all electron methods in disguise. For the Phillips-Kleinman and PAW pseudopotential methods we show that there is an explicit all electron reformulation (which is nearly equivalent). In the all electron reformulation, as part of the basis set, there are regular low wavevector basis wave functions (plane waves) and several, specially chosen, high wavevector basis wave functions that are specialized to the atomic environment relevant to nuclei of the substances studied. Using this as motivation, here we propose a new, PAW method motivated, basis set for small molecules, where we use the LO or lo (Localized Orbitals) basis wave functions, and pair them with a Gaussian basis, e.g. Gaussian Type Orbitals (GTO), for a hybrid basis for small molecules. Contracted Gaussian functions are also possible (CGFs). Several different, but related, LO (lo) basis wave functions are considered. We also show how to extend this idea to Slater basis set, Slater type orbitals (STO), instead of GTO orbitals, combined with LO or lo orbitals. This is done using shape functions.

physics.chem-ph↗

arXiv2024

Order parameters in quasi-1D spin systems

In this work we extend the notion of what is meant by a meanfield. Meanfields are approximately maps - through some self consistency relation - of a complex, usually manybody, problem to a simpler more readily solvable problem. This mapping can then be solved to represent properties of the complex many body problem using some self consistency relations. Prototypical examples of simpler meanfield problems (meanfield systems) are the single site and free particle problems. Here we propose a new class of simple meanfield systems where the simple problem to be solved is a 1D spin chain. These meanfields are particularly useful for studying quasi-1D models, where there is a 3D system composed of weakly coupled 1D spin chains with the coupling in the transverse direction weaker than in the 1D direction. We illustrate this idea by considering meanfields for the Ising (of any coupling sign) and ferromagnetic Heisenberg models with one direction coupled much more strongly then the other directions (quasi-1D systems) which map at meanfield level onto the 1D Ising and 1D ferromagnetic Heisenberg models. We also consider more exotic models to illustrate other methods of solving 1D systems, namely the $N$-state Potts model. Magnetic phase transition temperatures and are obtained for all three models, we see that they significantly differ from the usual meanfield estimates. Indeed if the 1D direction has coupling $Γ$ and the transverse directions have coupling $J$ with $λ\sim\fracΓ{J}\gg1$ then regular meanfield would predict the transition temperature to be $k_{B}T_{c}\simΓ$ for all three models while 1D meanfield predicts temperatures of $k_{B}T_{c}\sim\fracΓ{\log\left(λ\right)}$ for the Ising and Potts models and $k_{B}T_{c}\sim\fracΓ{\sqrtλ}$ for the ferromagnetic Heisenberg model. Cluster 1D meanfield extensions are also proposed.

cond-mat.stat-mech↗

arXiv2024

Multi-radius Soler-Williams Augmented Plane Waves (SAPWMR), Multi-Radius Soler-Williams Linearized Augmented Plane Waves (SLAPWMR) and extensions

In this work we present a new basis set for electronic structures (Density Functional Theory (DFT)) calculations. This basis set extends Soler Williams Linearized Augmented Plane Wave (SLAPW) basis sets by allowing variable Muffin Tin (MT) sphere radii for the different angular momentum channels and for different magnitude wave vectors of the augmented plane waves. With the correct choice of MT radius, this allows us to match additional derivatives of the wave function at the MT radius without having to resort to additional higher derivative terms as part of the wave function expansion inside the MT sphere. This should lead to low wave vector basis set and low linearization energy errors, arguably as good as APW basis set size and LAPW basis linearization errors. We call these basis sets SAPWMR and SLAPWMR depending on the number of derivative like wave functions kept inside the MT radii. Similarly local orbital (LO and lo basis wave functions depending on the number of derivative terms in the MT radius) are suggested with a variable radius. that reduces the number of derivative like terms needed to make them continuous or continuously differentiable. As such semi-core states can also be well handled by our methods. Furthermore in the appendix Full Potential Hamiltonian calculations (FLAPW) are extended to FSLAPWMR full potential calculations for Hamiltonian matrix elements. In the Appendix we introduce some further ideas to improve the speed of DFT calculations which are relevant to the basis sets presented here and to other basis sets such as the LAPW basis set.

cond-mat.other↗

arXiv2024

The Wilson-Fisher Fixed point revisited: importance of the form of the cutoff

In this work we re-examine the Wilson Fisher fixed point. We study Wilsonian momentum space renormalization group (RG) flow for various forms of the cutoff. We show that already at order $\left(4-d\right)^{1}$, where $d$ is the dimension of the $ϕ^{4}$ theory, there are changes to the position of the fixed point and the direction of irrelevant coupling parameters. We also show in a multi-flavor $ϕ^{4}$ model that symmetries of the Lagrange function can be destroyed if the different flavors have different cutoffs (that is the Lagrangian can flow to a non-symmetric fixed point). Some related comments are made about a similar situation in parquet RG (pRG). In future works we will study Wilsonian RG to order $\left(4-d\right)^{2}$ and find non-universal critical exponents that depend on the cutoff.

cond-mat.stat-mech↗

arXiv2024

One Axis Twisting (OAT) spin squeezing for metrology

In this work we study One Axis Twisting (OAT) spin squeezing for metrology in the presence of decoherence. We study Linbladian evolution in the presence of both T_1 and T_2 (longitudinal and transverse relaxation processes). We show that spin squeezing can be an effective way to improve metrological accuracy even in the presence of decoherence for OAT squeezing. We show our results are not sensitive to inhomogeneity of the squeezing strength of the many spin OAT Hamiltonian and that very general squeezed states do not have entanglement enhanced decoherence. We also extend the Kitagawa-Ueda OAT squeezing formula to finite polarization.

quant-ph↗

arXiv2024

Linearized analysis of dissipative Two Axis Counter Twisting (TACT) squeezing for Metrology

In this work we analyze two axis twisting in the presence of depolarizing channel dissipation. We find that spin squeezing is only possible if the dissipation is parametrically weaker than the squeezing coupling. Squeezing may be used for meteorologically useful decrease of spin noise but only in the case where the squeezing occurs before measurement, in the case one squeezes as one measures one also squeezes the signal thereby making spin squeezing ineffective for metrological gain. The key mathematical advance made in this work is the observation that TACT in the presence of depolarizing noise is equivalent to TACT with reduced polarization and no noise. We find an exponential gain in signal to noise with the exponent proportional to the ratio between the squeezing strength and the depolarization rate.

quant-ph↗