arXiv subjects

Shailesh Chandrasekharan

Publications and source records attributed to Shailesh Chandrasekharan.

At least 73 records · Page 4Linked to original sources

arXiv2010

Conductance of Quantum Impurity Models from Quantum Monte Carlo

The conductance of two Anderson impurity models, one with two-fold and another with four-fold degeneracy, representing two types of quantum dots, is calculated using a world-line quantum Monte Carlo (QMC) method. Extrapolation of the imaginary time QMC data to zero frequency yields the linear conductance, which is then compared to numerical renormalization group results in order to assess its accuracy. We find that the method gives excellent results at low temperature (T<Tk) throughout the mixed valence and Kondo regimes, but it is unreliable for higher temperature.

cond-mat.mes-hall↗

arXiv2010

Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind non-trivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical non-linear O(2) sigma model with a coupling $β$ and chemical potential $μ$ on a 2+1 dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at non-zero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of world-line of particles, the sign problem is absent and the model can be studied efficiently with the "worm algorithm". Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the $(β,μ)$ plane.

hep-lat↗

arXiv2009

Phase Transitions of S=1 Spinor Condensates in an Optical Lattice

We study the phase diagram of spin-one polar condensates in a two dimensional optical lattice with magnetic anisotropy. We show that the topological binding of vorticity to nematic disclinations allows for a rich variety of phase transitions. These include Kosterlitz-Thouless-like transitions with a superfluid stiffness jump that can be experimentally tuned to take a continuous set of values, and a new cascaded Kosterlitz-Thouless transition, characterized by two divergent length scales. For higher integer spin bosons S, the thermal phase transition out of the planar polar phase is strongly affected by the parity of S.

cond-mat.stat-mech↗

arXiv2009

The fermion bag approach to lattice field theories

We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons and there is no fermion permutation sign to worry about. We argue that as $U$ becomes finite fermions are liberated but are naturally confined to regions which we refer to as {\em fermion bags}. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three dimensional massless lattice Thirring model as an example we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find $ν=0.87(2)$ and $η=0.62(2)$.

hep-lat↗

arXiv2008

A new computational approach to lattice quantum field theories

Developments in algorithms over the past decade suggest that there is a new computational approach to a class of quantum field theories. This approach is based on rewriting the partition function in a representation similar to the world-line representation and hence we shall call it the "WL-approach". This approach is likely to be more powerful than the conventional approach in some regions of parameter space, especially in the presence of chemical potentials or massless fermions. While world-line representations are natural in the Hamiltonian formulation, they can also be constructed directly in Euclidean space. We first describe the approach and its advantages by considering the classical XY model in the presence of a chemical potential. We then argue that, $CP^{N-1}$ models, models of pions on the lattice and the lattice massless Thirring model, can all be formulated and solved using the WL-approach. In particular, we discover that the WL-approach to the Thirring model leads to a novel determinantal Monte-Carlo algorithm which we call the "dynamical-bag" algorithm. Finally, we argue that a simple extension of the WL-approach to gauge theories leads to a world-sheet, "WS-approach", in Abelian Lattice Gauge theory.

hep-lat↗

arXiv2008

Sigma-resonance and convergence of chiral perturbation theory

The dimensionless parameter $ξ' = M^2/(16 π^2 F^2)$, where $F$ is the pion decay constant in the chiral limit and $M$ is the pion mass at leading order in the quark mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $σ$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $ξ'$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calculated from the $ε$-regime and the $p$-regime. However, $ξ' \lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. However, for $ξ' > 0.0035$ the data begin to deviate qualitatively from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $σ$-resonance in our model. Our findings may be useful for lattice QCD studies.

hep-lat↗

arXiv2008

Role of the $σ$-resonance in determining the convergence of chiral perturbation theory

The dimensionless parameter $ξ= M_π^2/(16 π^2 F_π^2)$, where $F_π$ is the pion decay constant and $M_π$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $σ$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $ξ$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calculated from the $p$-regime and the $ε$-regime as expected. However, $ξ\lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. For $ξ> 0.0035$ the data begin to deviate dramatically from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $σ$-resonance in our model. Our findings may be useful for lattice QCD studies.

hep-lat↗

arXiv2008

Absence of vortex condensation in a two dimensional fermionic XY model

Motivated by a puzzle in the study of two dimensional lattice Quantum Electrodynamics with staggered fermions, we construct a two dimensional fermionic model with a global U(1) symmetry. Our model can be mapped into a model of closed packed dimers and plaquettes. Although the model has the same symmetries as the XY model, we show numerically that the model lacks the well known Kosterlitz-Thouless phase transition. The model is always in the gapless phase showing the absence of a phase with vortex condensation. In other words the low energy physics is described by a non-compact U(1) field theory. We show that by introducing an even number of layers one can introduce vortex condensation within the model and thus also induce a KT transition.

hep-lat↗

arXiv2007

Modeling pion physics in the $ε$-regime of two-flavor QCD using strong coupling lattice QED

In order to model pions of two-flavor QCD we consider a lattice field theory involving two flavors of staggered quarks interacting strongly with U(1) gauge fields. For massless quarks, this theory has an $SU_L(2)\times SU_R(2) \times U_A(1)$ symmetry. By adding a four-fermion term we can break the U_A(1) symmetry and thus incorporate the physics of the QCD anomaly. We can also tune the pion decay constant F, to be small compared to the lattice cutoff by starting with an extra fictitious dimension, thus allowing us to model low energy pion physics in a setting similar to lattice QCD from first principles. However, unlike lattice QCD, a major advantage of our model is that we can easily design efficient algorithms to compute a variety of quantities in the chiral limit. Here we show that the model reproduces the predictions of chiral perturbation theory in the $ε$-regime.

hep-lat↗

arXiv2007

Effects of the anomaly on the two-flavor QCD chiral phase transition

We use strongly coupled lattice QED with two flavors of massless staggered fermions to model the physics of pions in two-flavor massless QCD. Our model has the right chiral symmetries and can be studied efficiently with cluster algorithms. In particular we can tune the strength of the QCD anomaly and thus study its effects on the chiral phase transition. Our study confirms the widely accepted view point that the chiral phase transition is first order in the absence of the anomaly. Turning on the anomaly weakens the transition and turns it second order at a critical anomaly strength. The anomaly strength at the tricritical point is characterized using $r = (M_{η'}-M_π)/ρ_{η'}$ where $M_{η'}, M_π$ are the screening masses of the anomalous and regular pions and $ρ_{η'}$ is the mass-scale that governs the low energy fluctuations of the anomalous symmetry. We estimate that $r \sim 7 $ in our model. This suggests that a strong anomaly at the two-flavor QCD chiral phase transition is necessary to wash out the first order transition.

hep-lat↗

arXiv2006

Effects of the anomaly on the QCD chiral phase transition

We study a lattice field theory described by two flavors of massless staggered fermions interacting with U(1) gauge fields in the strong coupling limit. We show that the lattice model has a $SU(2)\times SU(2)\times U(1)$ chiral symmetry and can be used to model the two-flavor QCD chiral phase transition in the absence of the anomaly. It is also possible to add a coupling to this model which breaks the chiral symmetry to $SU(2)\times SU(2)$ and thus mimics the effects of the anomaly in two-flavor QCD. We construct an efficient directed loop algorithm to study such a model. We show that the chiral phase transition in our model is first order in the absence of the anomaly, while it becomes second order with O(4) exponents when the anomaly is turned on.

hep-lat↗

arXiv2006

Disorder-Induced Superfluidity in Hardcore Bosons in Two Dimensions

We study the effect of disorder on hardcore bosons in two dimensions at the SU(2) symmetric ``Heisenberg point''. We obtain our results with quantum Monte Carlo simulations using the directed loop algorithm. In the absence of disorder, the system has no long-range order at finite temperature due to the enhanced symmetry. However, the introduction of a disordered potential, uniformly distributed from -D to D, induces a finite-temperature superfluid phase. In particular the diagonal correlation length ξdecreases but the superfluid order-parameter correlation function becomes a power-law. A non-monotonic finite-size behavior is noted and explained as arising due to ξ. We provide evidence that at long distances the effects of a weak disordered potential can be mimicked by an effective uniform potential with a root-mean-square value: mu_eff = D/sqrt{3}. For strong disorder, the system becomes a Bose glass insulator.

cond-mat.stat-mech↗

arXiv2006

Anomalous superfluidity in 2+1 dimensional two-color lattice QCD

We study thermodynamics of strongly coupled lattice QCD with $two$ colors of staggered fermions in $(2+1)$ dimensions. The partition function of this model can be written elegantly as a statistical mechanics of dimers and baryonloops. The model is invariant under an $SO(3)\times U(1)$ symmetry. At low temperatures we find evidence for superfluidity in the U(1) symmetry sector while the SO(3) symmetry remains unbroken. The finite temperature phase transition appears to belong to the Kosterlitz-Thouless universality class, but the superfluid density jump $ρ_s(T_c)$ at the critical temperature $T_c$ is anomalously higher than the normal value of $2 T_c/π$. We show that by adding a small SO(3) symmetry breaking term to the model, the superfluid density jump returns to its normal value implying that the extra symmetry causes anomalous superfluid behavior. Our results may be of interest to researchers studying superfluidity in spin-1 systems.

hep-lat↗

arXiv2006

Quantum Phase Transitions of Hard-Core Bosons in Background Potentials

We study the zero temperature phase diagram of hard core bosons in two dimensions subjected to three types of background potentials: staggered, uniform, and random. In all three cases there is a quantum phase transition from a superfluid (at small potential) to a normal phase (at large potential), but with different universality classes. As expected, the staggered case belongs to the XY universality, while the uniform potential induces a mean field transition. The disorder driven transition is clearly different from both; in particular, we find z~1.4, ν~1, and β~0.6.

cond-mat.stat-mech↗

arXiv2006

Quantum Monte Carlo Study of Disordered Fermions

We study a strongly correlated fermionic model with attractive interactions in the presence of disorder in two spatial dimensions. Our model has been designed so that it can be solved using the recently discovered meron-cluster approach. Although the model is unconventional it has the same symmetries of the Hubbard model. Since the naive algorithm is inefficient, we develop a new algorithm by combining the meron-cluster technique with the directed-loop update. This combination allows us to compute the pair susceptibility and the winding number susceptibility accurately. We find that the s-wave superconductivity, present in the clean model, does not disappear until the disorder reaches a temperature dependent critical strength. The critical behavior as a function of disorder close to the phase transition belongs to the Berezinsky-Kosterlitz-Thouless universality class as expected. The fermionic degrees of freedom, although present, do not appear to play an important role near the phase transition.

cond-mat.str-el↗

arXiv2006

Phase-diagram of two-color lattice QCD in the chiral limit

We study thermodynamics of strongly coupled lattice QCD with two colors of massless staggered fermions as a function of the baryon chemical potential $μ$ in 3+1 dimensions using a new cluster algorithm. We find evidence that the model undergoes a weak first order phase transition at $μ=0$ which becomes second order at a finite $μ$. Symmetry considerations suggest that the universality class of these phase transitions should be governed by an $O(N)\times O(2)$ field theory with collinear order, with N=3 at $μ=0$ and N=2 at $μ\neq 0$. The universality class of the second order phase transition at $μ\neq 0$ appears to be governed by the decoupled XY fixed point present in the $O(2)\times O(2)$ field theory. Finally we show that the quantum (T=0) phase transition as a function of $μ$ is a second order mean field transition.

hep-lat↗

arXiv2006

Spectroscopy of the Kondo Problem in a Box

Motivated by experiments on double quantum dots, we study the problem of a single magnetic impurity confined in a finite metallic host. We prove an exact theorem for the ground state spin, and use analytic and numerical arguments to map out the spin structure of the excitation spectrum of the many-body Kondo-correlated state, throughout the weak to strong coupling crossover. These excitations can be probed in a simple tunneling-spectroscopy transport experiment; for that situation we solve rate equations for the conductance.

cond-mat.mes-hall↗

arXiv2005

On the Sign Problem in the Hirsch-Fye Algorithm for Impurity Problems

We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further use this insight to analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.

cond-mat.str-el↗