arXiv subjects

G J Sreejith

Publications and source records attributed to G J Sreejith.

At least 19 recordsLinked to original sources

arXiv2026

Group Convolutional Neural Network for the Low-Energy Spectrum in the Quantum Dimer Model

We obtain the $\rm{p4m}$-symmetric Group Convolutional Neural Network (GCNN) representations of the lowest energy eigenstate of the quantum dimer model on $L{\times} L$ square-lattice in each of the ${(L^2+18L+72)}/{8}$ irreducible representations (irreps) of the lattice space group and use these to investigate the competition between columnar, plaquette and mixed phases. The networks are optimized within each irrep by minimizing the energy, which is estimated from samples obtained via an efficient directed loop sampler. In extensive benchmarks, we show excellent agreement in energy estimates, order parameters and correlation functions with exact diagonalization or quantum Monte Carlo in systems of sizes $8\leq L\leq 32$. Analysis of the scaling of the gaps in different representation sectors with systems of sizes up to $L=32$ suggest a $4$-fold degenerate ground state for $V\leq 0.4$ narrowing the regime of possible mixed/plaquette phases to $0.4 < V< 1$. Our results show that GCNN is a powerful tool to investigate ground state phase diagrams. The approach paves the way for even more accurate results by producing highly accurate variational baseline wavefunctions for quantum Monte Carlo approaches.

cond-mat.dis-nn↗

arXiv2025

Full distribution and large deviations of local observables in an exactly solvable current carrying steady state of a strongly driven XXZ chain

Current carrying steady states of interacting spin chains exhibit rich structures generated through an interplay of constraints from the Hamiltonian dynamics and those induced by the current. The \textit{XXZ} spin chain when coupled to maximally polarizing Lindblad terms (with opposite signs on either end) admits an exact solution for the steady state in a matrix product state (MPS) form. We use this exact solution to study the correlations and distributions of local spin observables in the nonequilibrium steady state. We present exact expressions for spin correlators, entropy per site and scaled cumulant generating functions (SCGF) for distributions of local observables in the \textit{XX} limit (Ising anisotropy $Δ=0$). Further, we use the exact MPS solution in the $Δ>0$ regime, to calculate numerically exact entropy, correlations, as well as full distributions of spin observables in large systems. In systems where $Δ$ is a cosine of rational multiple of $π$, we can numerically exactly estimate the large system limit of the SCGF and the large deviation/rate functions of local-$z$ magnetization. For these, we show that the deviations of the SCGF, calculated in finite systems, from the asymptotic large system size limit decay exponentially with system size; however, the decay rate is a discontinuous function of $Δ$. The $x$ magnetization density shows a double peak structure at $Δ\lesssim 1$, suggesting short-range ferromagnetic ordering in the $x$ direction similar to what was reported for the ground state of the XXZ chain.

cond-mat.stat-mech↗

arXiv2023

Thermal Drude weight in an integrable chiral clock model

We calculate the finite temperature thermal conductivity of a time-reversal invariant chiral $\mathbb{Z}_3$ clock model along an integrable line in the parameter space using tDMRG. The thermal current itself is not a conserved charge, unlike in the XXZ model, but has a finite overlap with a local conserved charge $Q^{(2)}$ obtained from the transfer matrix. We find that the Drude weight is finite at non-zero temperature, and the Mazur bound from $Q^{(2)}$ saturates the Drude weight, allowing us to obtain an asymptotic expression for the Drude weight at high temperatures. The numerical estimates are validated using a sum rule for thermal conductivity. On the computational side, we also explore the effectiveness of the ancilla disentangler in the integrable and non-integrable regimes of the model. We find that the disentangler helps in localizing the entanglement growth around the quench location, but the improvement is lesser in the non-integrable regime and at low temperatures.

cond-mat.stat-mech↗

arXiv2023

Torus geometry eigenfunctions of an interacting multi-Landau level Hamiltonian

A short-ranged, rotationally symmetric multi-Landau-level model Hamiltonian for strongly interacting electrons in a magnetic field was proposed [A. Anand et al, Phys. Rev. Lett. 126, 136601 (2021)] with the key feature that it allows exact many-body eigenfunctions on the disk not just for quasiholes but for all charged and neutral excitations of the entire Jain sequence filling fractions. We extend this to geometries without full rotational symmetry, namely the torus and cylinder geometries, and present their spectra. Exact diagonalization of the interaction on the torus produces the low-energy spectra at filling fraction $ν=n/(2pn+1)$ that is identical, up to a topological $(2pn+1)$-fold multiplicity, to that of the integer quantum Hall spectra at $ν=n$, for the incompressible state as well as all excitations. While the ansatz eigenfunctions in the disk geometry cannot be generalized to closed geometries such as torus or sphere, we show how to extend them to cylinder geometry. Meanwhile, we show eigenfunctions for charged excitations at filling fractions between $\frac{1}{3}$ and $\frac{2}{5}$ can be written on the torus and the spherical geometries.

cond-mat.str-el↗

arXiv2022

Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods

Real-space entanglement spectrum (RSES) of a quantum Hall (QH) wavefunction gives a natural route to infer the nature of its edge excitations. Computation of RSES becomes expensive with an increase in the number of particles and included Landau levels (LL). RSES can be efficiently computed using Monte Carlo (MC) methods for trial states that can be written as products of determinants such as the composite fermion (CF) and parton states. This computational efficiency also applies to the RSES of lowest Landau level (LLL) projected CF and parton states; however, LLL projection to be used here requires approximations that generalize the Jain Kamilla (JK) projection. This work is a careful study of how this approximation should be made. We identify the approximation closest in spirit to JK projection and perform tests of the approximations involved in the projection by comparing the MC results with the RSES obtained from computationally expensive but exact methods. We present the techniques and use them to calculate the exact RSES of the exact LLL projected bosonic Jain $2/3$ state in bipartition of systems of sizes up to $N=24$ on the sphere. For the lowest few angular momentum sectors of the RSES, we present evidence to show that MC results closely match the exact spectra. We also discuss other plausible projection schemes. We also calculate the exact RSES of the unprojected fermionic Jain $2/5$ state obtained from the exact diagonalization of the Trugman-Kivelson Hamiltonian in the two lowest LLs on the sphere. By comparing with the RSES of the unprojected $2/5$ state from Monte Carlo methods, we show that the latter is practically exact.

cond-mat.str-el↗

arXiv2022

Energy transport in Z3 chiral clock model

We characterize the energy transport in a one dimensional $\mathbb{Z}_3$ chiral clock model. The model generalizes the $\mathbb{Z}_2$ symmetric transverse field Ising model (TFIM). The model is parametrized by a chirality parameter $θ$, in addition to $f$ and $J$ which are analogous to the transverse field and the nearest neighbour spin coupling in the TFIM. Unlike the well studied TFIM and XYZ models, does not transform to a fermionic system. We use a matrix product states implementation of the Lindblad master equation to obtain the non-equilibrium steady state (NESS) in systems of sizes up to $48$. We present the estimated NESS current and its scaling exponent $γ$ as a function of $θ$ at different $f/J$. The estimated $γ(f/J,θ)$ point to a ballistic energy transport along a line of integrable points $f=J\cos{3θ}$ in the parameter space; all other points deviate from ballistic transport. Analysis of finite size effects within the available system sizes suggest a diffusive behavior away from the integrable points.

cond-mat.stat-mech↗

arXiv2021

Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions

We argue and numerically substantiate that the real-space entanglement spectrum (RSES) of composite fermion quantum Hall states is given by the spectrum of a local boundary perturbation of a $(1+1)$d conformal field theory (CFT), which describes an effective edge dynamics along the real-space cut. The cut-and-glue approach suggests that the low-lying RSES is equivalent to the low-lying modes of some effective edge action. The general structure of this action is deduced by mapping to a boundary critical problem, generalizing work of Dubail, Read, and Rezayi [PRB 85, 11531 (2012)]. Using trial wave functions we numerically test our model of the RSES for the $ν= 2/3$ bosonic composite fermion state.

cond-mat.str-el↗

arXiv2021

Temperature dependent equilibration of spin orthogonal quantum Hall edge modes

Conductance of the edge modes as well as conductance across the co-propagating edge modes around the ν= 4/3, 5/3 and 2 quantum Hall states are measured by individually exciting the modes. Temperature dependent equilibration rates of the outer unity conductance edge mode are presented for different filling fractions. We find that the equilibration rate of the outer unity conductance mode at ν= 2 is higher and more temperature sensitive compared to the mode at fractional filling 5/3 and 4/3. At lowest temperature, equilibration length of the outer unity conductance mode tends to saturate with lowering filling fraction νby increasing magnetic field B. We speculate this saturating nature of equilibration length is arising from an interplay of Coulomb correlation and spin orthogonality.

cond-mat.mes-hall↗

arXiv2021

Cluster-cluster correlations beyond the Laughlin state

Number of zeros seen by a particle around small clusters of other particles is encoded in the root partition, and partly characterizes the correlations in fractional quantum Hall trial wavefunctions. We explore a generalization wherein we consider the counting of zeros seen by a cluster of particles on another cluster. Numbers of such zeros between clusters in the Laughlin wavefunctions are fully determined by the root partition. However, such a counting is unclear for general Jain states where a polynomial expansion is difficult. Here we consider the simplest state beyond the Laughlin wavefunction, namely a state containing a single quasiparticle of the Laughlin state. We show numerically and analytically that in the trial wavefunction for the quasiparticle of the Laughlin state, counting of zeros seen by a cluster on another cluster depends on the relative dimensions of the two clusters. We further ask if the patterns in the counting of zeros extend, in at least an approximate sense, to wavefunctions beyond the trial states. Using numerical computations in systems up to $N=9$, we present results for the statistical distribution of zeros around particle clusters at the center of an FQH droplet in the ground state of a Hamiltonian that is perturbed away from the $V_1$ interaction (short-range repulsion). Evolution of this distribution with the strength of the perturbation shows that the counting of zeros is altered by even a weak perturbation away from the parent Hamiltonian, though the perturbations do not change the phase of the system.

cond-mat.str-el↗

arXiv2021

Initializing ReLU networks in an expressive subspace of weights

Using a mean-field theory of signal propagation, we analyze the evolution of correlations between two signals propagating forward through a deep ReLU network with correlated weights. Signals become highly correlated in deep ReLU networks with uncorrelated weights. We show that ReLU networks with anti-correlated weights can avoid this fate and have a chaotic phase where the signal correlations saturate below unity. Consistent with this analysis, we find that networks initialized with anti-correlated weights can train faster (in a teacher-student setting) by taking advantage of the increased expressivity in the chaotic phase. Combining this with a previously proposed strategy of using an asymmetric initialization to reduce dead node probability, we propose an initialization scheme that allows faster training and learning than the best-known initializations.

cs.LG↗

arXiv2021

Post quench entropy growth in a chiral clock model

We numerically study quenches from a fully ordered state to the ferromagnetic regime of the chiral $\mathbb{Z}_3$ clock model, where the physics can be understood in terms of sparse domain walls of six flavors. As in the previously studied models, the spread of entangled domain wall pairs generated by the quench lead to a linear growth of entropy with time, upto a time $\ell/2v_g$ in size-$\ell$ subsystems in the bulk where $v_g$ is the maximal group velocity of domain walls. In small subsystems located in the bulk, the entropy continues to further grow towards $\ln 3$, as domain walls traverse the subsystem and increment the population of the two oppositely ordered states, restoring the $\mathbb{Z}_3$ symmetry. The latter growth in entropy is seen also in small subsystems near an open boundary in a non-chiral clock model. In contrast to this, in the case of the chiral model, the entropy of small subsystems near an open boundary saturates. We rationalize the difference in behavior in terms of qualitatively different scattering properties of domain walls at the open boundary in the chiral model. We also present empirical results for entropy growth, correlation spread, and energies of longitudinal-field-induced bound states of domain wall pairs in the chiral model.

cond-mat.stat-mech↗

arXiv2021

An Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

States of strongly interacting particles are of fundamental interest in physics, and can produce exotic emergent phenomena and topological structures. We consider here two-dimensional electrons in a magnetic field, and, departing from the standard practice of restricting to the lowest LL, introduce a model short-range interaction that is infinitely strong compared to the cyclotron energy. We demonstrate that this model lends itself to an exact solution for the ground as well as excited states at arbitrary filling factors $ν<1/2p$ and produces a fractional quantum Hall effect at fractions of the form $ν=n/(2pn+ 1)$, where n and p are integers. The fractional quantum Hall states of our model share many topological properties with the corresponding Coulomb ground states in the lowest Landau level, such as the edge physics and the fractional charge of the excitations.

cond-mat.str-el↗

arXiv2020

Magnetic field dependent equilibration of fractional quantum Hall edge modes

Fractional conductance is measured by partitioning $ν= 1$ edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the $ν= 1$ plateau respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance $e^2/3h$ arising from edge reconstruction. The results reveal remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing field.

cond-mat.mes-hall↗

arXiv2019

Scaling of Loschmidt echo in boundary driven critical Z-3 Potts model

Low frequency perturbations at the boundary of critical quantum chains can be understood in terms of the sequence of boundary conditions imposed by them, as has been previously demonstrated in the Ising and related fermion models. Using extensive numerical simulations, we explore the scaling behavior of the Loschmidt echo under longitudinal field perturbations at the boundary of a critical $\mathbb{Z}_3$ Potts model. We show that at times much larger than the relaxation time after a boundary quench, the Loschmidt-echo has a power-law scaling as expected from interpreting the quench as insertion of boundary condition changing operators. Similar scaling is observed as a function of time-period under a low frequency square-wave pulse. We present numerical evidence which indicate that under a sinusoidal or triangular pulse, scaling with time period is modified by Kibble-Zurek effect, again similar to the case of the Ising model. Results confirm the validity, beyond the Ising model, of the treatment of the boundary perturbations in terms of the effect on boundary conditions.

cond-mat.stat-mech↗

arXiv2018

Search for exact local Hamiltonians for general fractional quantum Hall states

We report on our systematic attempts at finding local interactions for which the lowest-Landau-level projected composite-fermion wave functions are the unique zero energy ground states. For this purpose, we study in detail the simplest non-trivial system beyond the Laughlin states, namely bosons at filling $ν=\frac{2}{3}$ and identify local constraints among clusters of particles in the ground state. By explicit calculation, we show that no Hamiltonian up to (and including) four particle interactions produces this state as the exact ground state, and speculate that this remains true even when interaction terms involving greater number of particles are included. Surprisingly, we can identify an interaction, which imposes an energetic penalty for a specific entangled configuration of four particles with relative angular momentum of $6\hbar$, that produces a unique zero energy solution (as we have confirmed for up to 12 particles). This state, referred to as the $λ$-state, is not identical to the projected composite-fermion state, but the following facts suggest that the two might be topologically equivalent: the two sates have a high overlap; they have the same root partition; the quantum numbers for their neutral excitations are identical; and the quantum numbers for the quasiparticle excitations also match. On the quasihole side, we find that even though the quantum numbers of the lowest energy states agree with the prediction from the composite-fermion theory, these states are not separated from the others by a clearly identifiable gap. This prevents us from making a conclusive claim regarding the topological equivalence of the $λ$ state and the composite-fermion state. Our study illustrates how new candidate states can be identified from constraining selected many particle configurations and it would be interesting to pursue their topological classification.

cond-mat.str-el↗

arXiv2018

Temporal order in periodically driven spins in star-shaped clusters

We experimentally study the response of star-shaped clusters of initially unentangled $N=4$, 10 and 37 nuclear spin-$\frac{1}{2}$ moments to an inexact $π$-pulse sequence, and show that an Ising coupling between the centre and the satellite spins results in robust period-two magnetization oscillations. The period is stable against bath-effects but the amplitude decays with a time scale that depends on the inexactness of the pulse. Simulations reveal a semiclassical picture where the rigidity of the period is due to a randomizing effect of the Larmor precession under the magnetization of surrounding spins. The time scales with stable periodicity increase with net initial magnetization even in the presence of perturbations, indicating a robust temporal ordered phase for large systems with finite magnetization per spin.

cond-mat.stat-mech↗

arXiv2017

Surprising robustness of particle-hole symmetry for composite fermion liquids

We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at $1/3$ and $2/3$. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.

cond-mat.str-el↗

arXiv2016

Parafermion chain with $2π/k$ Floquet edge modes

We study parafermion chains with $\mathbb{Z}_k$ symmetry subject to a periodic binary drive. We focus on the case $k=3$. We find that the chains support different Floquet edge modes at nontrivial quasienergies, distinct from those for the static system. We map out the corresponding phase diagram by a combination of analytics and numerics, and provide the location of $2π/3$ modes in parameter space. We also show that the modes are robust to weak disorder. While the previously studied $\mathbb{Z}_2$-invariant Majorana systems posesses a transparent weakly interacting case where the existence of a $π$-Majorana mode is manifest, our intrinsically strongly interacting generalization demonstrates that the existence of such a limit is not necessary.

cond-mat.stat-mech↗