arXiv subjects

Arpita Goswami

Publications and source records attributed to Arpita Goswami.

7 recordsLinked to original sources

arXiv2026

Subsystem localization in a two-leg ladder system

We consider a ladder system where one leg, referred to as the ``bath", is governed by an Aubry-André (AA) type Hamiltonian, while the other leg, termed the ``subsystem", follows a standard tight-binding Hamiltonian. We investigate the localization properties in the subsystem induced by its coupling to the bath. For the coupling strength larger than a critical value ($t'>t'_c$), the analysis of the static properties shows that there are three distinct phases as the AA potential strength $V$ is varied: a fully delocalized phase at low $V$, a localized phase at intermediate $V$, and a weakly delocalized (fractal) phase at large $V$. The fractal phase also appears in a narrow region along the boundary between the delocalized and localized phases. An analysis of the projected wavepacket dynamics in the subsystem shows that the delocalized phase exhibits a ballistic behavior, whereas the weakly delocalized phase is subdiffusive. Interestingly, the narrow fractal phase shows a super- to subdiffusive behavior as we go from the delocalized to localized phase. When $t'<t'_c$, the intermediate localized phase disappears, and we find a delocalized (ballistic) phase at low $V$ and a weakly delocalized (subdiffusive) phase at large $V$. Between those two phases, there is also an anomalous crossover regime where the system can be super- or subdiffusive. Beyond the ballistic phase observed at low $V$, we also identify a superdiffusive regime emerging in the limit $t'/V \ll 1$, which continuously approaches the ballistic behavior as $t' \to 0$. Finally, in some limiting scenario, we also establish a mapping between our ladder system and a well-studied one-dimensional generalized Aubry-André (GAA) model.

cond-mat.stat-mech↗

arXiv2026

Anderson localization via Peierls phase modulation

We investigate a two leg ladder system subjected to an external magnetic field. In the absence of a magnetic field, the system is described by a clean tight binding model, with no disorder in either the onsite potential or the hopping amplitudes. The effect of magnetic field in this system is studied by introducing the Peierls phases in the hopping amplitudes along a leg (appropriate when the Landau gauge is chosen). For a uniform magnetic field, characterized by a constant Peierls phase, we find that all eigenstates remain delocalized. In contrast, random Peierls phases, representing a random magnetic field, lead to complete localization of the eigenstates. We further show that a quasiperiodic modulation of the Peierls phase can drive a transition from a fully delocalized to a fully localized phase upon tuning the quasiperiodicity. For a two parameter quasiperiodic Peierls phase, varying analogously to a generalized Aubry Andre type potential, we construct the phase diagram of the system. The phase diagram exhibits regions of delocalized and localized phases, separated by intermediate regimes of mixed phase. We also perform a semiclassical analysis that qualitatively yields a similar phase diagram, capturing the localization transition. Our results demonstrate a mechanism for controlling transport properties via the Peierls phase engineering.

cond-mat.dis-nn↗

arXiv2026

Exact mobility edges in a slowly varying quasiperiodic ladder model

We propose a minimal two-leg ladder model in which the mobility edge (ME) arises solely due to bond modulation, introduced through a slowly varying quasiperiodic modulation in the inter-leg tunnelling amplitudes. We demonstrate that this bond-modulated ladder naturally hosts two propagation channels, whose symmetric and antisymmetric combinations experience opposite effective onsite potentials, unlike the one-dimensional quasiperiodic models with onsite modulations. Using the adiabatic (slowly varying) limit of the modulation, we derive an exact analytical condition for the single-particle mobility edge, $E_c=\pm|2t-λ|,$ where $t$ is the hopping amplitude along both the legs and $λ$ is the bond modulation strength. This result directly generalizes the classic ME condition for slowly varying onsite potentials to a multi-leg (two-leg in our case) geometry. Extensive numerical calculations, including inverse participation ratios, Lyapunov exponents, density of states, and participation-ratio scaling, demonstrate excellent agreement with the analytical prediction across a wide range of parameters. We further identify a regime for small modulation exponents $0 < ν<1$, where localized and weakly delocalized states coexist even beyond the transition point ($λ_c=2t$). Our results establish that a deterministic bond modulation can serve as a sufficient ingredient to produce an exact ME in ladder systems, offering experimentally accessible routes toward tuning nonergodic extended phases.

cond-mat.stat-mech↗

arXiv2026

Fluctuation-stable generalized entropy probes of spectral heterogeneity

Generalized entropy measures are widely used to characterize localization and multifractality, and the regime $q>1$ is often empirically found to exhibit improved numerical stability and cleaner scaling behavior. Here, we develop a fluctuation-stability framework for generalized entropy diagnostics and show that weak-amplitude spectral fluctuations are amplified for $q<1$ and suppressed for $q>1$, thereby providing a theoretical basis for the physically robust $q>1$ regime. A thermodynamic scaling analysis further identifies an asymptotically stable regime beyond a critical threshold. As an application, we introduce the entropy-gradient susceptibility $χ_q$ as a coarse-grained probe of spectral heterogeneity. Using the Aubry-André and generalized Aubry-André models, we demonstrate that $χ_q$ sharply distinguishes homogeneous localization transitions from mobility-edge coexistence regimes. Our results establish fluctuation stability as a guiding principle for generalized entropy diagnostics in quasiperiodic systems.

cond-mat.stat-mech↗

arXiv2026

Information Theoretic Signatures of Localization and Mobility Edges in Quasiperiodic Systems

We investigate localization transitions and mobility edge phenomena in one-dimensional quasiperiodic lattice models using an information theoretic framework based on the Tsallis entropy of single particle eigenstates.We employ the Tsallis entropy as a continuous, normalized functional of wavefunction amplitudes, where the entropic index $q$ provides a tunable sensitivity to different regions of the probability distribution, enhancing the contribution of localized peaks ($q>1$) or extended components ($q<1$). Building on this framework, we introduce an entropy-gradient susceptibility defined from the energy dependence of the Tsallis entropy, which probes variations in eigenstate structure across the spectrum. We show that this quantity clearly distinguishes global localization transitions from mobility edge physics. In the Aubry Andre model, where all eigenstates undergo a uniform transition, the entropy varies smoothly, resulting in a broad crossover in the susceptibility. In contrast, in systems hosting mobility edges, including a quasiperiodically modulated Su Schrieffer Heeger chain and the generalized Aubry Andre model, the coexistence of localized and extended states produces sharp spectral variations, leading to a pronounced and system size independent peak. The qualitative behavior persists over a broad range of the entropic parameter $q$, with systematic variations reflecting its role as a tunable probe of spectral structure. Our results establish an information theoretic approach that leverages the continuous $q$ dependence of Tsallis entropy to construct a derivative based measure of spectral heterogeneity, providing a complementary and physically transparent diagnostic of mobility edge phenomena beyond conventional state resolved measures.

cond-mat.stat-mech↗

arXiv2025

Nonextensive Thermodynamics of the Morse Oscillator: Signature and Solid State Application

In this work, we present a detailed thermodynamic analysis of a bound quantum system: the Morse oscillator within the framework of Tsallis nonextensive statistics. Using the property of the bound spectrum (upper bound) of the Morse potential, limited by the bond dissociation energy, we analytically derive the generalized partition function. We present results for both the high- and low-temperature limits. We propose the effective number of accessible states as a measure of nonextensivity. The calculation shows that the nonextensive framework further restricts the number of accessible states. We also derive the generalized internal energy and entropy and examine their dependence on temperature and the nonextensivity parameter $ q $. Numerical results confirm the strong effect of nonextensive behavior in the low-temperature regime (precisely low to moderate temperature), where the ratio of generalized internal energy and internal energy calculated from the Boltzmann Gibbs (BG) formula develops a nontrivial dip structure for $ q < 1 $. Moreover, the generalized specific heat shows the Schottky-type anomaly. We extend our study by deriving the specific heat of solids with BG and Tsallis statistics using the anharmonic energy levels of the Morse oscillator. This study suggests that the Morse oscillator is a solvable and physically meaningful testing ground for exploring the thermodynamics of quantum systems driven by nonextensive statistics, with implications for the vibrational properties of the non-equilibrium molecular thermodynamics (especially diatomic molecules).

cond-mat.stat-mech↗

arXiv2025

Phase transitions in $q$-state clock model

The $q-$state clock model, sometimes called the discrete $XY$ model, is known to show a second-order (symmetry breaking) phase transition in two-dimension (2D) for $q\le 4$ ($q=2$ corresponds to the Ising model). On the other hand, the $q\to\infty$ limit of the model corresponds to the $XY$ model, which shows the infinite order (non-symmetry breaking) Berezinskii-Kosterlitz-Thouless (BKT) phase transition in 2D. Interestingly, the 2D clock model with $q\ge 5$ is predicted to show three different phases and two associated phase transitions. There are varying opinions about the actual characters of phases and the associated transitions. In this work, we develop the basic and higher-order mean-field (MF) theories to study the $q$-state clock model systematically. Our MF calculations reaffirm that, for large $q$, there are three phases: (broken) $\mathbb{Z}_q$ symmetric ferromagnetic phase at the low temperature, emergent $U(1)$ symmetric BKT phase at the intermediate temperature, and paramagnetic (disordered) phase at the high temperature. The phase transition at the higher temperature is found to be of the BKT type, and the other transition at the lower temperature is argued to be a large-order spontaneous symmetry-breaking (SSB) type (the largeness of transition order yields the possibility of having some of the numerical characteristics of a BKT transition). The higher-order MF theory developed here better characterizes phases by estimating the spin-spin correlation between two neighbors.

cond-mat.stat-mech↗