arXiv subjects

Nishan Ranabhat

Publications and source records attributed to Nishan Ranabhat.

10 recordsLinked to original sources

arXiv2026

Dynamical signatures of deconfined spinons in dimerized sawtooth chains

We study the ground-state properties and dynamical response of the Heisenberg model on the sawtooth chain in and away from the exactly solvable valence-bond-solid (VBS) point. We employ U(1)-symmetric density-matrix renormalization group (DMRG) and time-dependent variational principle (TDVP) methods to compute equilibrium diagnostics and the zero-temperature dynamical structure factor (DSF) $S^{zz}(q,ω)$ across the dimerized phase, a valence-bond-ordered state in which the two symmetry-equivalent apex--base bonds of each triangle develop unequal spin correlations, probing the approach to the continuous lower phase boundary, the exact VBS point, and the approach to the first-order upper boundary. In every regime, the DSF is a broad continuum dominated by a bright band at its lower edge, with the intensity at the one-triplon energy $ω\simeq J_{AB}$ suppressed. We identify the spectrum as a deconfined two-spinon continuum of kink and antikink domain walls between the two degenerate singlet coverings. Closed-form spinon dispersions fix the continuum edges and track the dominant band across the zone in all three regimes, while an explicit finite-separation two-kink calculation in a constrained Hilbert space reproduces the measured intensity distribution. Our results provide a microscopic picture of fractionalized excitations in the dimerized sawtooth chain and are relevant to the recently discovered Ti$^{3+}$ kagome fluorides, where strongly anisotropic exchange interactions can generate sawtooth-chain building blocks.

cond-mat.str-el↗

arXiv2026

Quantum complexity across thermal phase transition in the transverse field Ising chain with long-range couplings

We investigate the behavior of the Schmidt gap, the von Neumann entanglement entropy, and the non-stabiliserness in proximity to the classical phase transition of the one-dimensional long-range transverse-field Ising model (LRTFIM). Leveraging the time-dependent variational principle (TDVP) within a tensor-network formulation, we simulate thermal states through their purified tensor-network representations. Our results show that these observables, typically regarded as hallmarks of quantum criticality, exhibit pronounced and coherent signatures even at a classical thermal transition, highlighting the emergence of quantum complexity as the system nears thermal criticality.

cond-mat.str-el↗

arXiv2026

Probability-Phase Mutual Information

Quantum coherence is an exquisitely quantum phenomenon that depends on both probability amplitudes and relative phases. Standard coherence measures quantify superposition within density matrices but cannot distinguish ensembles that produce the same mixed state through different distributions of pure states. Building on the geometric formulation of quantum mechanics, we introduce the probability-phase mutual information $I(P;Φ)$. We show that it characterizes quantum coherence at the ensemble level and that ensemble coherence systematically exceeds density-matrix coherence, thus quantifying the structure lost when averaging over pure states. Eventually, its relevance for quantum thermodynamics, quantum information theory, and deep thermalization is highlighted by explicit examples: canonical ensembles reveal temperature-dependent probability-phase correlations absent from thermal density matrices; we show that the probability of converting an ensemble into another one is bound by the ratio of their $I(P;Φ)$; and, that a non-vanishing $I(P;Φ)$ signals the breakdown of deep thermalization.

quant-ph↗

arXiv2025

Non-classicality at equilibrium and efficient predictions under non-commuting charges

A quantum thermodynamic system can conserve non-commuting observables, but the consequences of this phenomenon on relaxation are still not fully understood. We investigate this problem by leveraging an observable-dependent approach to equilibration and thermalization in isolated quantum systems. We extend such approach to scenarios with non-commuting charges, and show that it can accurately estimate the equilibrium distribution of coarse observables without access to the energy eigenvalues and eigenvectors. Our predictions do not require weak coupling and are not restricted to local observables, thus providing an advantage over the non-Abelian thermal state. Within this approach, weak values and quasiprobability distributions emerge naturally and play a crucial role in characterizing the equilibrium distributions of observables. We show and numerically confirm that, due to charges' non-commutativity, these weak values can be anomalous even at equilibrium, which has been proven to be a proxy for non-classicality. Our work thus uncovers a novel connection between the relaxation of observables under non-commuting charges, weak values, and Kirkwood-Dirac quasiprobability distributions.

quant-ph↗

arXiv2025

Large-scale portfolio optimization with variational neural annealing

Portfolio optimization is a routine asset management operation conducted in financial institutions around the world. However, under real-world constraints such as turnover limits and transaction costs, its formulation becomes a mixed-integer nonlinear program that current mixed-integer optimizers often struggle to solve. We propose mapping this problem onto a classical Ising-like Hamiltonian and solving it with Variational Neural Annealing (VNA), via its classical formulation implemented using autoregressive neural networks. We demonstrate that VNA can identify near-optimal solutions for portfolios comprising more than 2,000 assets and yields performance comparable to that of state-of-the-art optimizers, such as Mosek, while exhibiting faster convergence on hard instances. Finally, we present a dynamical finite-size scaling analysis applied to the S&P 500, Russell 1000, and Russell 3000 indices, revealing universal behavior and polynomial annealing time scaling of the VNA algorithm on portfolio optimization problems.

cond-mat.dis-nn↗

arXiv2025

Tensor Network Techniques for Quantum Computation

This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics are covered, including tensor structures and network representations like Matrix Product States (MPS) and Tree Tensor Networks (TTN). These preliminaries provide readers with the core mathematical tools and concepts necessary for quantum physics and quantum computing applications, bridging the gap between multi-linear algebra and complex quantum systems. Part II explores practical applications of tensor networks in simulating quantum dynamics, with a particular focus on the efficiency they offer for systems of high computational complexity. Key topics include Hamiltonian dynamics, quantum annealing, open system dynamics, and optimization strategies using TN frameworks. A final chapter addresses the emerging role of "quantum magic" in tensor networks. It delves into non-stabilizer states and their contribution to quantum computational power beyond classical simulability, featuring methods such as stabilizer-enhanced MPS and the Clifford-dressed TDVP.

quant-ph↗

arXiv2025

Beginner's Lecture Notes on Quantum Spin Chains, Exact Diagonalization and Tensor Networks

Aimed at introducing readers to the physics of strongly correlated many-body systems, these notes focus on numerical methods, with detailed discussions on implementing working code for exact diagonalization. A brief introduction to tensor network methods is also included. Prepared for the Summer School Quantumandu, held at Tribhuvan University (Kathmandu, Nepal) from 25 to 31 July 2024, as part of the ICTP's Physics Without Frontiers program, these notes are primarily intended for readers encountering this field for the first time.

cond-mat.str-el↗

arXiv2025

Dynamical deconfinement transition driven by density of excitations

We investigate the deconfinement transition driven by excitations in long-range spin models. At low temperatures, these models exhibit a confined phase where domain-wall (or kinks) are localized. As temperature increases, kinks interact and propagate, leading to a transition to a de-confined phase. This transition is influenced by the interplay between thermal energy and interaction effects, resulting in extended, de-confined regions. Although kinks density is dynamically stable, non-equilibrium changes in their fluctuations characterize the transition. Our findings provide insights into the mechanisms of confinement and deconfinement in long-range spin models, with implications for both condensed matter physics and lattice gauge theories. Bridging these fields, this study sheds light on the universal aspects of confinement and opens avenues for further exploration and experimental verification.

cond-mat.str-el↗

arXiv2023

Thermalization of long range Ising model in different dynamical regimes: a full counting statistics approach

We study thermalization of transverse field Ising chain with power law decaying interaction $\sim 1/r^α$ following a global quantum quench of the transverse field to two different dynamical regimes. We quantify the thermalization behavior by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the Gibbs canonical ensemble (GCE). To this end, we use matrix product state (MPS) based time dependent variational principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all the interaction strength $α$ considered whereas thermalization occurs in the region with weak confinement.

cond-mat.stat-mech↗

arXiv2022

Dynamics of the order-parameter statistics in the long-range Ising model

We study the relaxation of the local ferromagnetic order in the transverse field quantum Ising chain with power-law decaying interactions $1/r^α$. We prepare the system in the GHZ state and study the time evolution of the probability distribution function (PDF) of the order-parameter within a block of $l$ when quenching the transverse field. The model is known to support long-range order at finite temperature for $α\leq 2.0$ . In this regime, quasi-localized topological magnetic defects are expected to strongly affect the equilibration of the full probability distribution. We highlight different dynamical regimes where gaussification mechanism may be slowed down by confinement and eventually breaks. We further study the PDF dynamics induced by changing the effective dimensionality of the system; we mimic this by quenching the range of the interactions. As a matter of fact, the behavior of the system crucially depends on the value of $α$ governing the unitary evolution.

cond-mat.str-el↗