arXiv subjects

Shailesh Chandrasekharan

Publications and source records attributed to Shailesh Chandrasekharan.

At least 55 records · Page 3Linked to original sources

arXiv2016

Solution to sign problems in models of interacting fermions and quantum spins

We show that solutions to fermion sign problems in the CT-INT formulation can be extended to systems involving fermions interacting with dynamical quantum spins. While these sign problems seem unsolvable in the auxiliary field approach, solutions emerge in the worldline representation of quantum spins. Combining the idea with meron-cluster methods, we are able to extend the solvable models even further. We demonstrate these novel solutions to sign problems by considering several examples of strongly correlated systems.

cond-mat.str-el↗

arXiv2016

Solution to the sign problem in a frustrated quantum impurity model

In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in half the space we show that all negative weight configurations can be eliminated. This pairing naturally leads to the original frustrated quantum spin model at half filling and thus solves its sign problem.

cond-mat.str-el↗

arXiv2016

Fermion masses through four-fermion condensates

Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.

hep-lat↗

arXiv2015

Origin of fermion masses without spontaneous symmetry breaking

Using a simple three dimensional lattice four-fermion model we argue that massless fermions can become massive due to interactions without the need for any spontaneous symmetry breaking. Using large scale Monte Carlo calculations within our model, we show that this non-traditional mass generation mechanism occurs at a second order quantum critical point that separates phases with the same symmetries. Universality then suggests that the new origin for the fermion mass should be of wide interest.

hep-lat↗

arXiv2014

Fermion Bags and A New Origin for a Fermion Mass

The fermion bag is a powerful idea that helps to solve fermion lattice field theories using Monte Carlo methods. Some sign problems that had remained unsolved earlier can be solved within this framework. In this work we argue that the fermion bag also gives insight into a new mechanism of fermion mass generation, especially at strong couplings where fermion masses are related to the fermion bag size. On the other hand, chiral condensates arise due to zero modes in the Dirac operator within a fermion bag. Although in traditional four-fermion models the two quantities seem to be related, we show that they can be decoupled. While fermion bags become small at strong couplings, the ability of zero modes of the Dirac operator within fermion bags to produce a chiral condensate, can be suppressed by the presence of additional zero modes from other fermions. Thus, fermions can become massive even without a chiral condensate. This new mechanism of mass generation was discovered long ago in lattice field theory, but has remained unappreciated. Recent work suggests that it may be of interest even in continuum quantum field theory.

hep-lat↗

arXiv2014

Solution to new sign problems with Hamiltonian Lattice Fermions

We present a solution to the sign problem in a class of particle-hole symmetric Hamiltonian lattice fermion models on bipartite lattices using the idea of fermion bags. The solution remains valid when the particle-hole symmetry is broken through a staggered chemical potential term. This solution allows, for the first time, simulations of some massless four-fermion models with minimal fermion doubling and with an odd number of fermion flavors using ultra-local actions. One can thus study a variety of quantum phase transitions that have remained unexplored so far due to sign problems.

hep-lat↗

arXiv2014

Massive fermions without fermion bilinear condensates

We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The model contains a $SU(4)$ symmetry which forbids non-zero fermion bilinear mass terms, due to which there is a massless fermion phase at weak couplings. However, even at strong couplings fermion bilinear condensates do not appear in our model, although fermions do become massive. While the existence of this exotic strongly coupled massive fermion phase was established long ago, the nature of the transition between the massless and the massive phase has remained unclear. Using Monte Carlo calculations in three space-time dimensions, we find evidence for a direct second order transition between the two phases suggesting that the exotic lattice phase may have a continuum limit at least in three dimensions. A similar exotic second order critical point was found recently in a bilayer system on a honeycomb lattice.

hep-lat↗

arXiv2013

Solution to sign problems in half-filled spin-polarized electronic systems

We solve the sign problem in a particle-hole symmetric spin-polarized fermion model on bipartite lattices using the idea of fermion bags. The solution can be extended to a class of models at half filling but without particle-hole symmetry. Attractive Hubbard models with an odd number of fermion species can also be solved. The new solutions should allow us to study quantum phase transitions that have remained unexplored so far due to sign problems.

cond-mat.str-el↗

arXiv2013

Quantum critical behavior in three dimensional lattice Gross-Neveu models

We study quantum critical behavior in three dimensional lattice Gross-Neveu models containing two massless Dirac fermions. We focus on two models with SU(2) flavor symmetry and either a $Z_2$ or a U(1) chiral symmetry. Both models could not be studied earlier due to sign problems. We use the fermion bag approach which is free of sign problems and compute critical exponents at the phase transitions. We estimate $ν= 0.83(1)$, $η= 0.62(1)$, $η_ψ= 0.38(1)$ in the $Z_2$ and $ν= 0.849(8)$, $η= 0.633(8)$, $η_ψ= 0.373(3)$ in the U(1) model.

hep-lat↗

arXiv2013

Fermion Bag Approach to Fermion Sign Problems

The fermion bag approach is a new method to tackle fermion sign problems in lattice field theories. Using this approach it is possible to solve a class of sign problems that seem unsolvable by traditional methods. The new solutions emerge when partition functions are written in terms of fermion bags and bosonic worldlines. In these new variables it is possible to identify hidden pairing mechanisms which lead to the solutions. The new solutions allow us for the first time to use Monte Carlo methods to solve a variety of interesting lattice field theories, thus creating new opportunities for understanding strongly correlated fermion systems.

hep-lat↗

arXiv2012

Solutions to sign problems in lattice Yukawa models

We prove that sign problems in the traditional approach to some lattice Yukawa models can be completely solved when the fermions are formulated using fermion bags and the bosons are formulated in the worldline representation. We prove this within the context of two examples of three dimensional models, symmetric under $U_L(1) \times U_R(1) \times Z_2 ({Parity})$ transformations, one involving staggered fermions and the other involving Wilson fermions. We argue that these models have interesting quantum phase transitions that can now be studied using Monte Carlo methods.

hep-lat↗

arXiv2012

Fermion bag solutions to some sign problems in four-fermion field theories

Lattice four-fermion models containing $N$ flavors of staggered fermions, that are invariant under $Z_2$ and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. Here we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.

hep-lat↗

arXiv2012

Fermion bags, duality and the three dimensional massless lattice Thirring model

The recently proposed fermion bag approach is a powerful technique to solve some four-fermion lattice field theories. Due to the existence of a duality between strong and weak couplings, the approach leads to efficient Monte Carlo algorithms in both these limits. The new method allows us for the first time to accurately compute quantities close to the quantum critical point in the three dimensional lattice Thirring model with massless fermions on large lattices. The critical exponents at the quantum critical point are found to be $ν=0.85(1)$, $η= 0.65(1)$ and $η_ψ= 0.37(1)$.

hep-lat↗

arXiv2011

The generalized fermion-bag approach

We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a bag. Paired fermions usually act like bosons and do not lead to sign problems. A resummation of all unpaired fermion degrees of freedom inside the bag is sufficient to solve the fermion sign problem in a variety of interesting cases. Using a concept of duality we then argue that the size of the fermion bags is small both at strong and weak couplings. This allows us to construct efficient algorithms in both these limits. Using the fermion bag approach, we study the quantum phase transition of the 3D massless lattice Thirrring model which is of interest in the context of Graphene. Using our method we are able to solve the model on lattices as large as $40^3$ with moderate computational resources. We obtain the precise location of the quantum critical point and the values of the critical exponents through this study.

hep-lat↗

arXiv2011

Partition Functions of Strongly Correlated Electron Systems as "Fermionants"

We introduce a new mathematical object, the "fermionant" ${\mathrm{Ferm}}_N(G)$, of type $N$ of an $n \times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces to the determinant. The partition function of the repulsive Hubbard model, of geometrically frustrated quantum antiferromagnets, and of Kondo lattice models can be expressed as fermionants of type N=2, which naturally incorporates infinite on-site repulsion. A computation of the fermionant in polynomial time would solve many interesting fermion sign problems.

cond-mat.str-el↗

arXiv2010

Anomaly and a QCD-like phase diagram with massive bosonic baryons

We study a strongly coupled $Z_2$ lattice gauge theory with two flavors of quarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times \mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD with two flavors of quarks without an anomaly. The model also contains a coupling that can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCD anomaly. At low temperatures $T$ and small baryon chemical potential $μ_B$ the model contains massless pions and massive bosonic baryons similar to QCD with an even number of colors. In this work we study the $T-μ_B$ phase diagram of the model and show that it contains three phases : (1) A chirally broken phase at low $T$ and $μ_B$, (2) a chirally symmetric baryon superfluid phase at low $T$ and high $μ_B$, and (3) a symmetric phase at high $T$. We find that the nature of the finite temperature chiral phase transition and in particular the location of the tricritical point that seperates the first order line from the second order line is affected significantly by the anomaly.

hep-lat↗

arXiv2010

Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions

We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that complex bags with positive and negative weights come with almost equal probabilities and this leads to a severe sign problem. On the other hand simple bags mostly have a positive weight. Since the complex bags almost cancel each other, we suggest that eliminating them from the partition function may be a good approximation. This modified partition function suffers only from a mild sign problem. We also find a simpler model which does not suffer from any sign problem and may still be a good approximation at small and intermediate values of the hopping parameter. We also prove that when the hopping parameter is strictly infinite all fermion bags are non-negative.

hep-lat↗

arXiv2010

Quantum Phase Transition and Dynamically Enhanced Symmetry in Quadruple Quantum Dot System

We propose a system of four quantum dots designed to study the competition between three types of interactions: Heisenberg, Kondo and Ising. We find a rich phase diagram containing two sharp features: a quantum phase transition (QPT) between charge-ordered and charge-liquid phases, and a dramatic resonance in the charge liquid visible in the conductance. The QPT is of the Kosterlitz-Thouless type with a discontinuous jump in the conductance at the transition. We connect the resonance phenomenon with the degeneracy of three levels in the isolated quadruple dot and argue that this leads to a Kondo-like dynamical enhancement of symmetry from U(1) x Z_2 to U(1) x U(1).

cond-mat.mes-hall↗