arXiv subjects

S. Chandrasekharan

Publications and source records attributed to S. Chandrasekharan.

At least 19 recordsLinked to original sources

arXiv2014

Progress towards quantum simulating the classical O(2) model

We connect explicitly the classical $O(2)$ model in 1+1 dimensions, a model sharing important features with $U(1)$ lattice gauge theory, to physical models potentially implementable on optical lattices and evolving at physical time. Using the tensor renormalization group formulation, we take the time continuum limit and check that finite dimensional projections used in recent proposals for quantum simulators provide controllable approximations of the original model. We propose two-species Bose-Hubbard models corresponding to these finite dimensional projections at strong coupling and discuss their possible implementations on optical lattices using a $^{87}$Rb and $^{41}$K Bose-Bose mixture.

hep-lat↗

arXiv2009

Ground State and Excitations of Quantum Dots with "Magnetic Impurities"

We consider an "impurity" with a spin degree of freedom coupled to a finite reservoir of non-interacting electrons, a system which may be realized by either a true impurity in a metallic nano-particle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong and weak coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity susceptibility and the local susceptibility. Extensive quantum Monte-Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir -- the "clean Kondo box" model -- we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parity and for the canonical and grand-canonical ensembles.

cond-mat.mes-hall↗

arXiv2007

From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition

Using a loop-cluster algorithm we investigate the spin 1/2 Heisenberg antiferromagnet on a square lattice with exchange coupling $J$ and an additional four-spin interaction of strength $Q$. We confirm the existence of a phase transition separating antiferromagnetism at $J/Q > J_c/Q$ from a valence bond solid (VBS) state at $J/Q < J_c/Q$. Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as $80^2$, we find evidence for a weak first order phase transition. We also present a detailed study of the antiferromagnetic phase. For $J/Q > J_c/Q$ the staggered magnetization, the spin stiffness, and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at $J/Q < J_c/Q$, and we show that long but finite antiferromagnetic correlations are still present.

cond-mat.str-el↗

arXiv2006

Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD

The order parameter of a finite system with a spontaneously broken continuous global symmetry acts as a quantum mechanical rotor. Both antiferromagnets with a spontaneously broken $SU(2)_s$ spin symmetry and massless QCD with a broken $SU(2)_L \times SU(2)_R$ chiral symmetry have rotor spectra when considered in a finite volume. When an electron or hole is doped into an antiferromagnet or when a nucleon is propagating through the QCD vacuum, a Berry phase arises from a monopole field and the angular momentum of the rotor is quantized in half-integer units.

cond-mat.other↗

arXiv2004

An Introduction to Chiral Symmetry on the Lattice

The $SU(N_f)_L \otimes SU(N_f)_R$ chiral symmetry of QCD is of central importance for the nonperturbative low-energy dynamics of light quarks and gluons. Lattice field theory provides a theoretical framework in which these dynamics can be studied from first principles. The implementation of chiral symmetry on the lattice is a nontrivial issue. In particular, local lattice fermion actions with the chiral symmetry of the continuum theory suffer from the fermion doubling problem. The Ginsparg-Wilson relation implies Lüscher's lattice variant of chiral symmetry which agrees with the usual one in the continuum limit. Local lattice fermion actions that obey the Ginsparg-Wilson relation have an exact chiral symmetry, the correct axial anomaly, they obey a lattice version of the Atiyah-Singer index theorem, and still they do not suffer from the notorious doubling problem. The Ginsparg-Wilson relation is satisfied exactly by Neuberger's overlap fermions which are a limit of Kaplan's domain wall fermions, as well as by Hasenfratz and Niedermayer's classically perfect lattice fermion actions. When chiral symmetry is nonlinearly realized in effective field theories on the lattice, the doubling problem again does not arise. This review provides an introduction to chiral symmetry on the lattice with an emphasis on the basic theoretical framework.

hep-lat↗

arXiv2004

Nonlinear Realization of Chiral Symmetry on the Lattice

We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the doubler fermions while maintaining exact chiral symmetry on the lattice. Our lattice formulation enables us to address non-perturbative questions in effective field theories of baryons interacting with pions and in models involving constituent quarks interacting with pions and gluons. We show that a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering complex action problems. In our formulation one can also decide non-perturbatively if the chiral quark model of Georgi and Manohar provides an appropriate low-energy description of QCD. If so, one could understand why the non-relativistic quark model works.

hep-lat↗

arXiv2003

D-Theory: Field Quantization by Dimensional Reduction of Discrete Variables

D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical gauge fields are replaced by quantum links. The classical fields of a d-dimensional quantum field theory reappear as low-energy effective degrees of freedom of the discrete variables, provided the (d+1)-dimensional D-theory is massless. When the extent of the extra Euclidean dimension becomes small in units of the correlation length, an ordinary d-dimensional quantum field theory emerges by dimensional reduction. The D-theory formulation of scalar field theories with various global symmetries and of gauge theories with various gauge groups is constructed explicitly and the mechanism of dimensional reduction is investigated.

hep-lat↗

arXiv2003

Lattice Theories with Nonlinearly Realized Chiral Symmetry

We present the lattice formulation of effective Lagrangians in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework both the Wilson term removing unphysical doubler fermions and the fermion mass term do not break chiral symmetry. Our lattice formulation allows us to address non-perturbative questions in effective theories of baryons interacting with pions and in models involving constitutent quarks interacting with pions and gluons. With the presented methods, a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering a complex action problem. This might lead to new insights into the phase diagram of strongly interacting matter at non-zero chemical potential.

hep-lat↗

arXiv2003

QCD at Fixed Topology

Since present Monte Carlo algorithms for lattice QCD may become trapped in a fixed topological charge sector, it is important to understand the effect of calculating at fixed topology. In this work, we show that although the restriction to a fixed topological sector becomes irrelevant in the infinite volume limit, it gives rise to characteristic finite size effects due to contributions from all $θ$-vacua. We calculate these effects and show how to extract physical results from numerical data obtained at fixed topology.

hep-lat↗

arXiv2002

Meron-Cluster Approach to Systems of Strongly Correlated Electrons

Numerical simulations of strongly correlated electron systems suffer from the notorious fermion sign problem which has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we show how the fermion sign problem can be solved completely with meron-cluster methods in a large class of models of strongly correlated electron systems, some of which are in the extended Hubbard model family and show s-wave superconductivity. In these models we also find that on-site repulsion can even coexist with a weak chemical potential without introducing sign problems. We argue that since these models can be simulated efficiently using cluster algorithms they are ideal for studying many of the interesting phenomena in strongly correlated electron systems.

cond-mat.str-el↗

arXiv2001

From Spin Ladders to the 2-d O(3) Model at Non-Zero Density

The numerical simulation of various field theories at non-zero chemical potential suffers from severe complex action problems. In particular, QCD at non-zero quark density can presently not be simulated for that reason. A similar complex action problem arises in the 2-d O(3) model -- a toy model for QCD. Here we construct the 2-d O(3) model at non-zero density via dimensional reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The complex action problem of the 2-d O(3) model manifests itself as a sign problem of the ladder system. This sign problem is solved completely with a meron-cluster algorithm.

hep-lat↗

arXiv2001

Physical Observables from Lattice QCD at Fixed Topology

Because present Monte Carol algorithms for lattice QCD may become trapped in a given topological charge sector when one approaches the continuum limit, it is important to understand the effect of calculating at fixed topology. In this work, we show that although the restriction to a fixed topological sector becomes irrelevant in the infinite volume limit, it gives rise to characteristic finite size effects due to contributions from all $θ$-vacua. We calculate these effects and show how to extract physical results from numerical data obtained at fixed topology.

hep-lat↗

arXiv2001

Solution of the Complex Action Problem in the Potts Model for Dense QCD

Monte Carlo simulations of lattice QCD at non-zero baryon chemical potential $μ$ suffer from the notorious complex action problem. We consider QCD with static quarks coupled to a large chemical potential. This leaves us with an SU(3) Yang-Mills theory with a complex action containing the Polyakov loop. Close to the deconfinement phase transition the qualitative features of this theory, in particular its Z(3) symmetry properties, are captured by the 3-d 3-state Potts model. We solve the complex action problem in the Potts model by using a cluster algorithm. The improved estimator for the $μ$-dependent part of the Boltzmann factor is real and positive and is used for importance sampling. We localize the critical endpoint of the first order deconfinement phase transition line and find consistency with universal 3-d Ising behavior. We also calculate the static quark-quark, quark-anti-quark, and anti-quark-anti-quark potentials which show screening as expected for a system with non-zero baryon density.

hep-lat↗

arXiv2000

Flop Transitions in Cuprate and Color Superconductors: From SO(5) to SO(10) Unification?

The phase diagrams of cuprate superconductors and of QCD at non-zero baryon chemical potential are qualitatively similar. The Neel phase of the cuprates corresponds to the chirally broken phase of QCD, and the high-temperature superconducting phase corresponds to the color superconducting phase. In the SO(5) theory for the cuprates the $SO(3)_s$ spin rotational symmetry and the $U(1)_{em}$ gauge symmetry of electromagnetism are dynamically unified. This suggests that the $SU(2)_L \otimes SU(2)_R \otimes U(1)_B$ chiral symmetry of QCD and the $SU(3)_c$ color gauge symmetry may get unified to SO(10). Dynamical enhancement of symmetry from $SO(2)_s \otimes \Z(2)$ to $SO(3)_s$ is known to occur in anisotropic antiferromagnets. In these systems the staggered magnetization flops from an easy 3-axis into the 12-plane at a critical value of the external magnetic field. Similarly, the phase transitions in the SO(5) and SO(10) models are flop transitions of a ``superspin''. Despite this fact, a renormalization group flow analysis in $4-ε$ dimensions indicates that a point with full SO(5) or SO(10) symmetry exists neither in the cuprates nor in QCD.

hep-lat↗

arXiv1999

Meron-Cluster Simulation of Quantum Spin Ladders in a Magnetic Field

Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Meron-cluster algorithms lead to an efficient solution of sign problems for both fermionic and bosonic models. Here we apply the meron concept to quantum spin systems in an arbitrary external magnetic field, in which case standard cluster algorithms fail. As an example, we simulate antiferromagnetic quantum spin ladders in a uniform external magnetic field that competes with the spin-spin interaction. The numerical results are in agreement with analytic predictions for the magnetization as a function of the external field.

cond-mat.stat-mech↗

arXiv1999

Meron-Cluster Simulation of a Chiral Phase Transition with Staggered Fermions

We examine a (3+1)-dimensional model of staggered lattice fermions with a four-fermion interaction and Z(2) chiral symmetry using the Hamiltonian formulation. This model cannot be simulated with standard fermion algorithms because those suffer from a very severe sign problem. We use a new fermion simulation technique - the meron-cluster algorithm - which solves the sign problem and leads to high-precision numerical data. We investigate the finite temperature chiral phase transition and verify that it is in the universality class of the 3-d Ising model using finite-size scaling.

hep-lat↗

arXiv1998

Non-perturbative Renormalization Constants using Ward Identities

We extend the application of vector and axial Ward identities to calculate $b_A$, $b_P$ and $b_T$, coefficients that give the mass dependence of the renormalization constants of the corresponding bilinear operators in the quenched theory. The extension relies on using operators with non-degenerate quark masses. It allows a complete determination of the $O(a)$ improvement coefficients for bilinears in the quenched approximation using Ward Identities alone. Only the scale dependent normalization constants $Z_P^0$ (or $Z_S^0$) and $Z_T$ are undetermined. We present results of a pilot numerical study using hadronic correlators.

hep-lat↗

arXiv1998

Green's Functions from Quantum Cluster Algorithms

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a cluster algorithm for the partition function has been constructed. To explain the idea, we consider the quantum XY model and compute its two point Green's function in various ways, showing that all of them are equivalent. We also provide numerical evidence confirming the analytic arguments. Similar techniques are applicable to other models. In particular, in the recently constructed quantum link models, the new technique allows us to construct improved estimators for Wilson loops and may lead to a very precise determination of the glueball spectrum.

cond-mat.stat-mech↗