arXiv subjects

Abhishek Samlodia

Publications and source records attributed to Abhishek Samlodia.

9 recordsLinked to original sources

arXiv2026

Fast Scrambling in the Hyperbolic Ising Model

We investigate many-body chaos and scrambling in the Hyperbolic Ising model, a mixed-field Ising model living in the background of AdS2. The effect of the curvature is captured by site-dependent couplings obtained from the AdS2 metric applied to a flat nearest-neighbor spin chain. Using a combination of out-of-time-ordered correlators (OTOCs), Krylov complexity, and spectral statistics, we present consistent evidence that this model exhibits faster scrambling behavior relative to its flat counterpart. In particular, we observe signatures consistent with fast scrambling dynamics emerging from purely local interactions. At the system sizes accessible to tensor network simulations, the OTOCs display short-lived exponential growth regimes, from which we extract effective Lyapunov exponents. These effective finite-size exponents exhibit a temperature dependence broadly compatible with the Maldacena-Shenker-Stanford (MSS) bound within numerical uncertainty. Our results indicate that increasing spatial curvature can significantly decrease scrambling time in systems with only nearest-neighbor interactions, providing a minimal and computationally accessible platform for studying quantum chaos. This makes the model a promising test-bed for exploring scrambling and operator growth in near-term quantum simulation architectures.

quant-ph↗

arXiv2026

Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using Matrix Product States (MPS) and Matrix Product Operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure Out of time Ordered Correlators (OTOCs) to explore the scrambling behavior of the theory.

hep-lat↗

arXiv2025

Symmetries and Anomalies of Hamiltonian Staggered Fermions

We review the shift (translation) and time reversal symmetries of Hamiltonian staggered fermions and their connection to continuum symmetries concentrating in particular on the case of massless fermions and (3+1) dimensions. We construct operators using the staggered fields that implement these symmetries on finite lattices. We show that shifts composed of an odd multiple of the elementary shift anti-commute with time reversal and are related to continuum axial transformations. We argue that the presence of these non-trivial commutation relations implies the existence of lattice 't Hooft anomalies. From the shifts we also construct a set of conserved, quantized charges that generate continuous symmetries of the lattice theory. In general these do not commute with the vector charge signaling further 't Hooft anomalies.

hep-lat↗

arXiv2024

Fermions, quantum gravity and holography in two dimensions

We study a model comprising $N$ flavors of Kähler Dirac fermion propagating on a triangulated two dimensional disk which is constrained to have a negative average bulk curvature. Dirichlet boundary conditions are chosen for the fermions. Quantum fluctuations of the geometry are included by summing over all possible triangulations consistent with these constraints. We show in the limit $N\to \infty$ that the partition function is dominated by a regular triangulation of two dimensional hyperbolic space. We use strong coupling expansions and Monte Carlo simulation to show that in this limit boundary correlators of the fermions have a power law dependence on boundary separation as one expects from holography. However we argue that this behavior breaks down for any finite number of massive fields in the thermodynamic limit and quantum fluctuations of the bulk geometry drive the theory into a non-holographic phase. In contrast, for massless fermions we find evidence that the boundary is conformal even for finite $N$. This is consistent with theoretical results in quantum Liouville theory.

hep-lat↗

arXiv2024

Phase diagram of generalized XY model using tensor renormalization group

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless (BKT) and Ising class. We explore the model for a wide range of temperatures, $T$, and the deformation parameter, $Δ$, and compute specific heat along with integer and half-integer magnetic susceptibility, finding both BKT-like and Ising-like transitions and the region where they meet.

hep-lat↗

arXiv2023

GPU-Acceleration of Tensor Renormalization with PyTorch using CUDA

We show that numerical computations based on tensor renormalization group (TRG) methods can be significantly accelerated with PyTorch on graphics processing units (GPUs) by leveraging NVIDIA's Compute Unified Device Architecture (CUDA). We find improvement in the runtime and its scaling with bond dimension for two-dimensional systems. Our results establish that the utilization of GPU resources is essential for future precision computations with TRG.

hep-lat↗

arXiv2023

Deconfinement Phase Transition in Bosonic BMN Model at General Coupling

We present our analysis of the deconfinement phase transition in the bosonic BMN matrix model. The model is investigated using a non-perturbative lattice framework. We used the Polyakov loop as the order parameter to monitor the phase transition, and the results were verified using the separatrix ratio. The calculations are performed using a large number of colors and a broad range of temperatures for all couplings. Our results indicate a first-order phase transition in this theory for all the coupling values that connect the perturbative and non-perturbative regimes of the theory.

hep-lat↗

arXiv2023

Investigating the Two-Dimensional Generalized XY Model using Tensor Networks

The critical behavior of the two-dimensional XY model has been explored in the literature using various methods. They include the high-temperature expansion (HTE) method, Monte Carlo (MC) approach, strong coupling expansion method, and tensor network (TN) methods. This model undergoes a Berezinskii-Kosterlitz-Thouless (BKT) type of phase transition. This model can be modified by adding spin-nematic interaction terms with a period to give rise to the generalized XY model. The modified model contains excitations of integer and half-integer vortices. These vortices govern the critical behavior of the theory and produce rich physics. With the help of tensor networks, we investigate the transition behavior between the integer vortex binding and half-integer vortex binding phases of the model and how this transition line merges into two BKT transition lines.

hep-lat↗

arXiv2022

Non-perturbative phase structure of the bosonic BMN matrix model

We study the bosonic part of the BMN matrix model for wide ranges of temperatures, values of the deformation parameter, and numbers of colors $16 \leq N \leq 48$. Using lattice computations, we analyze phase transitions in the model, observing a single first-order transition from a uniform to a gapped phase for all values of the deformation parameter. We study the functional form of the dependence of the critical temperature on the deformation parameter, to describe how our results smoothly interpolate between the limits of the bosonic BFSS model and the gauged Gaussian model.

hep-lat↗