arXiv subjects

Shailesh Chandrasekharan

Publications and source records attributed to Shailesh Chandrasekharan.

At least 91 records · Page 5Linked to original sources

arXiv2005

Chiral limit of 2-color QCD at strong couplings

We study two-color lattice QCD with massless staggered fermions in the strong coupling limit using a new and efficient cluster algorithm. We focus on the phase diagram of the model as a function of temperature $T$ and baryon chemical potential $μ$ by working on $L_t \times L^d$ lattices in both $d=2,3$. In $d=3$ we find that at $μ=0$ the ground state of the system breaks the global U(2) symmetry present in the model to U(1), while the finite temperature phase transition (with $L_t=4$) which restores the symmetry is a weak first order transition. In $d=2$ we find evidence for a novel phase transition similar to the Berezinky-Kosterlitz-Thouless phenomena. On the other hand the quantum (T=0) phase transition to a symmetric phase as a function of $μ$ is second order in both $d=2,3$ and belongs to the mean field universality class.

hep-lat↗

arXiv2005

Mesoscopic Kondo Problem

We study the effect of mesoscopic fluctuations on a magnetic impurity coupled to a spatially confined electron gas with a temperature in the mesoscopic range (i.e. between the mean level spacing $Δ$ and the Thouless energy $E_{\rm Th}$). Comparing ``poor-man's scaling'' with exact Quantum Monte Carlo, we find that for temperatures larger than the Kondo temperature, many aspects of the fluctuations can be captured by the perturbative technique. Using this technique in conjunction with semi-classical approximations, we are able to calculate the mesoscopic fluctuations for a wide variety of systems. For temperatures smaller than the Kondo temperature, we find large fluctuations and deviations from the universal behavior.

cond-mat.mes-hall↗

arXiv2005

Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics

Nanoscale physics and dynamical mean field theory have both generated increased interest in complex quantum impurity problems and so have focused attention on the need for flexible quantum impurity solvers. Here we demonstrate that the mapping of single quantum impurity problems onto spin-chains can be exploited to yield a powerful and extremely flexible impurity solver. We implement this cluster algorithm explicitly for the Anderson and Kondo Hamiltonians, and illustrate its use in the ``mesoscopic Kondo problem''. To study universal Kondo physics, a large ratio between the effective bandwidth $D_\mathrm{eff}$ and the temperature $T$ is required; our cluster algorithm treats the mesoscopic fluctuations exactly while being able to approach the large $D_\mathrm{eff}/T$ limit with ease. We emphasize that the flexibility of our method allows it to tackle a wide variety of quantum impurity problems; thus, it may also be relevant to the dynamical mean field theory of lattice problems.

cond-mat.mes-hall↗

arXiv2004

Failure of Mean Field Theory at Large N

We study strongly coupled lattice QCD with $N$ colors of staggered fermions in 3+1 dimensions. While mean field theory describes the low temperature behavior of this theory at large $N$, it fails in the scaling region close to the finite temperature second order chiral phase transition. The universal critical region close to the phase transition belongs to the 3d XY universality class even when $N$ becomes large. This is in contrast to Gross-Neveu models where the critical region shrinks as $N$ (the number of flavors) increases and mean field theory is expected to describe the phase transition exactly in the limit of infinite $N$. Our work demonstrates that close to second order phase transitions infrared fluctuations can sometimes be important even when $N$ is strictly infinite.

hep-lat↗

arXiv2004

A Multi-level Algorithm for Quantum-impurity Models

A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low temperatures, the new algorithm has many advantages over conventional algorithms. For example, the model can be easily simulated in the Kondo limit without time discretization errors. Further, many observables including the impurity susceptibility and a variety of fermionic observables can be calculated efficiently. Finally the new approach allows us to explore a general technique, called the multi-level algorithm, to solve the sign problem. We find that the multi-level algorithm is able to generate an exponentially large number of configurations with an effort that grows as a polynomial in inverse temperature such that configurations with a positive sign dominate over those with negative signs. Our algorithm can be easily generalized to other multi-impurity problems.

cond-mat.str-el↗

arXiv2004

Connecting Lattice QCD with Chiral Perturbation Theory at Strong Coupling

We study the difficulties associated with detecting chiral singularities predicted by chiral perturbation theory (ChPT) in lattice QCD. We focus on the physics of the remnant O(2) chiral symmetry of staggered fermions in the strong coupling limit using the recently discovered directed path algorithm. Since it is easier to look for power-like singularities as compared to logarithmic ones, our calculations are performed at a fixed finite temperature in the chirally broken phase. We show that the behavior of the chiral condensate, the pion mass and the pion decay constant, for small masses, are all consistent with the predictions of ChPT. However, the values of the quark masses that we need to demonstrate this are much smaller than those being used in dynamical QCD simulations. We also need to use higher order terms in the chiral expansion to fit our data.

hep-lat↗

arXiv2003

Chiral and Critical Behavior in Strong Coupling QCD

We use a cluster algorithm to study the critical behavior of strongly coupled lattice QCD in the chiral limit. We show that the finite temperature chiral phase transition belongs to the O(2) universality class as expected. When we compute the finite size effects of the chiral susceptibility in the low temperature phase close to the transition, we find clear evidence for chiral singularities predicted by chiral perturbation theory (ChPT). On the other hand it is difficult to reconcile the quark mass dependence of various quantities near the chiral limit with ChPT.

hep-lat↗

arXiv2003

Chiral Limit of Strongly Coupled Lattice QCD at Finite Temperatures

We use the recently proposed directed-path algorithm to study the chiral limit of strongly coupled lattice QCD with staggered quarks at finite temperatures. The new algorithm allows us to compute the chiral susceptibility and the pion decay constant accurately on large lattices for massless quarks. In the low temperature phase we find clear evidence for the singularities predicted by chiral perturbation theory. We also show convincingly that the chiral phase transition is of second order and belongs to the O(2) universality class.

hep-lat↗

arXiv2003

Kosterlitz Thouless Universality in Dimer Models

Using the monomer-dimer representation of strongly coupled U(N) lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in (2+1) dimensions. A new cluster algorithm allows us to compute monomer-monomer and dimer-dimer correlations at zero monomer density (chiral limit) accurately on large lattices. This makes it possible to show convincingly, for the first time, that these models undergo a finite temperature phase transition which belongs to the Kosterlitz-Thouless universality class. We find that this universality class is unaffected even in the large N limit. This shows that the mean field analysis often used in this limit breaks down in the critical region.

hep-lat↗

arXiv2003

Chiral Limit of Strongly Coupled Lattice Gauge Theories

We construct a new and efficient cluster algorithm for updating strongly coupled U(N) lattice gauge theories with staggered fermions in the chiral limit. The algorithm uses the constrained monomer-dimer representation of the theory and should also be of interest to researchers working on other models with similar constraints. Using the new algorithm we address questions related to the chiral limit of strongly coupled U(N) gauge theories beyond the mean field approximation. We show that the infinite volume chiral condensate is non-zero in three and four dimensions. However, on a square lattice of size $L$ we find $\sum_x < \barψψ(x) \barψψ(0) > \sim L^{2-η}$ for large $L$ where $η= 0.420(3)/N + 0.078(4)/N^2$. These results differ from an earlier conclusion obtained using a different algorithm. Here we argue that the earlier calculations were misleading due to uncontrolled autocorrelation times encountered by the previous algorithm.

hep-lat↗

arXiv2002

Chiral Limit of Staggered Fermions at Strong Couplings: A Loop Representation

The partition function of two dimensional massless staggered fermions interacting with U(N) gauge fields is rewritten in terms of loop variables in the strong coupling limit. We use this representation of the theory to devise a non-local Metropolis algorithm to calculate the chiral susceptibility. For small lattices our algorithm reproduces exact results quite accurately. Applying this algorithm to large volumes yields rather surprising results. In particular we find $m_π\neq 0$ for all $N$ and it increases with $N$. Since the talk was presented we have found reasons to believe that our algorithm breaks down for large volumes questioning the validity of our results.

hep-lat↗

arXiv2002

Unexpected Results in the Chiral Limit with Staggered Fermions

A cluster algorithm is constructed and applied to study the chiral limit of the strongly coupled lattice Schwinger model involving staggered fermions. The algorithm is based on a novel loop representation of the model. Finite size scaling of the chiral susceptibility based on data from lattices of size up to $64\times 64$ indicates the absence of long range correlations at strong couplings. Assuming that there is no phase transition at a weaker coupling, the results imply that all mesons acquire a mass at non-zero lattice spacings. Although this does not violate any known physics, it is surprising since typically one expects a single pion to remain massless at non-zero lattice spacings in the staggered fermion formulation.

hep-lat↗

arXiv2001

Superconductivity and Chiral Symmetry Breaking with Fermion Clusters

Cluster variables have recently revolutionized numerical work in certain models involving fermionic variables. This novel representation of fermionic partition functions is continuing to find new applications. After describing results from a study of a two dimensional Hubbard type model that confirm a superconducting transition in the Kosterlitz-Thouless universality class, we show how a cluster type algorithm can be devised to study the chiral limit of strongly coupled lattice gauge theories with staggered fermions.

hep-lat↗

arXiv2001

Novel Quantum Monte Carlo Algorithms for Fermions

Recent research shows that the partition function for a class of models involving fermions can be written as a statistical mechanics of clusters with positive definite weights. This new representation of the model allows one to construct novel algorithms. We illustrate this through models consisting of fermions with and without spin. A Hubbard type model with both attractive and repulsive interactions becomes tractable using the new approach. Precision results in the two dimensional attractive model confirm a superfluid phase transition in the Kosterlitz-Thouless universality class.

hep-lat↗

arXiv2001

Kosterlitz-Thouless Universality in a Fermionic System

A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous calculations in the attractive Hubbard model which were limited to small lattices, the new algorithm is used to study the critical behavior on lattices as large as $128\times 128$. These precise results for the first time show that a fermionic system can undergo a finite temperature phase transition whose critical behavior is well described by the predictions of Kosterlitz and Thouless almost three decades ago. In particular it is confirmed that the spatial winding number susceptibility obeys the well known predictions of finite size scaling for $T<T_c$ and up to logarithmic corrections the pair susceptibility scales as $L^{2-η}$ at large volumes with $0\leqη\leq 0.25$ for $0\leq T\leq T_c$.

cond-mat.str-el↗

arXiv2000

QCD at a Finite Density of Static Quarks

Recently, cluster methods have been used to solve a variety of sign problems including those that arise in the presence of fermions. In all cases an analytic partial re-summation over a class of configurations in the path integral was necessary. Here the new ideas are illustrated using the example of QCD at a finite density of static quarks. In this limit the sign problem simplifies since the fermionic part decouples. Furthermore, the problem can be solved completely when the gauge dynamics is replaced by a Potts model. On the other hand in QCD with light quarks the solution will require a partial re-summation over both fermionic and gauge degrees of freedom. The new approach points to unexplored directions in the search for a solution to this more challenging sign problem.

hep-lat↗

arXiv2000

Critical Behavior of a Chiral Condensate with a Meron Cluster Algorithm

A new meron cluster algorithm is constructed to study the finite temperature critical behavior of the chiral condensate in a $(3+1)$ dimensional model of interacting staggered fermions. Using finite size scaling analysis the infinite volume condensate is shown to be consistent with the behavior of the form $(T_c-T)^{0.314(7)}$ for temperatures less than the critical temperature and $m^{1/4.87(10)}$ at the critical temperature confirming that the critical behavior belongs to the 3-d Ising universality class within one to two sigma deviation. The new method, along with improvements in the implementation of the algorithm, allows the determination of the critical temperature $T_c$ more accurately than was possible in a previous study.

hep-lat↗

arXiv2000

SO(10) Unification of Color Superconductivity and Chiral Symmetry Breaking?

Motivated by the SO(5) theory of high-temperature superconductivity and antiferromagnetism, we ask if an SO(10) theory unifies color superconductivity and chiral symmetry breaking in QCD. The transition to the color superconducting phase would then be analogous to a spin flop transition. While the spin flop transition generically has a unified SO(3) description, the SO(5) and SO(10) symmetric fixed points are unstable, at least in (4 - epsilon) dimensions, and require the fine-tuning of one additional relevant parameter. If QCD is near the SO(10) fixed point, it has interesting consequences for heavy ion collisions and neutron stars.

hep-ph↗