arXiv subjects

Mohammad Pouranvari

Publications and source records attributed to Mohammad Pouranvari.

At least 19 recordsLinked to original sources

arXiv2025

Helical Quasiperiodic Chains with Engineered Dissipation: Liouvillian Rapidity Diagnostics of Transport and Localization

We study relaxation spectra of a quadratic spinless--fermion helical chain with an Aubry--Andre--type quasiperiodic potential and a single N--th neighbor (helical) hopping. Dissipation and pumping are introduced via local linear Lindblad jump operators and treated exactly using the third--quantization / Majorana covariance formalism. Focusing on periodic boundary conditions (to avoid edge artefacts) we compute the Liouvillian rapidities and their smallest nonzero real part (the rapidity gap) for several spatial dissipation patterns: uniform (all), single--site (one--site) and two--site (two--site) placement, plus pairwise gain/loss on helical partner sites. We show that uniform dissipation yields large, weakly lambda--dependent gaps, while sparse local dissipation produces gaps that shrink rapidly as the quasiperiodic potential lambda induces localization. Increasing t_N enhances relaxation by improving mode overlap with dissipative channels. Finite--size scaling, rapidity level statistics (Poisson vs Wigner--Dyson), and spatial profiles of slow modes provide a consistent picture linking Liouvillian spectral structure to transport and localization. Our results highlight Liouvillian rapidities as compact, experimentally relevant diagnostics of relaxation and sensitivity in engineered open quantum lattices.

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arXiv2025

Phase Structure and Machine Learning Identification in One Dimensional Systems with Power Law Correlated Disorder and Long Range Hopping

We investigate a one-dimensional tight-binding model in which onsite potentials $\{\varepsilon_i\}$ exhibit power-law spatialcorrelations (with exponent $\alpha$) and the hopping amplitudes decay as $t_{ij}\sim |i-j|^{-\beta}$. This two-parameter family interpolates continuously between short-range Anderson-like disorder, correlated disorder with conventional hopping, and long-range hopping models with nontrivial delocalization tendencies. Using large-scale exact diagonalization, we construct a comprehensive phase map in the $(\alpha,\beta)$ plane by combining spectral statistics, density-of-states analysis, and energy-resolved localization indicators such as the participation ratio, single-particle entanglement entropy, level-spacing ratio $r$, and the ratio of the geometric to arithmetic density of states. From these observables we define phase-indicator functions that compactly quantify localization behavior across the spectrum. Our analysis reveals robust mobility edges and multiple regimes of spectral coexistence between localized, extended, resonant, and critical states. Finite-size scaling, implemented via an explicit smoothness-based cost function, enables extraction of critical exponents and delineation of transition lines across the $(\alpha,\beta)$ parameter space. To validate and complement these physics-based diagnostics, we employ a supervised autoencoder that learns high-level representations of eigenstate structure directly from raw features and reliably reproduces the phase classification defined by the indicator functions. Together, these approaches provide a coherent and internally consistent picture of the spectral transitions driven by correlated disorder and long-range hopping, establishing a unified framework for characterizing mobility edges in long-range one-dimensional systems.

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arXiv2025

Phase Transitions and Critical Behavior in Quasi-One-Dimensional Two-Channel Systems with Quasiperiodic Disorder

We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-André model. By analyzing the Lyapunov exponent and localization length, we characterize the phase transitions and critical behavior of the system. For the symmetric model, we obtain the phase diagram for the entire spectrum, revealing mobility edges between delocalized and localized states. In contrast, for the asymmetric model, we identify a critical line $ λ_1^c + λ_2^c \approx 0.5 $ marking the phase transition between delocalized and localized states. We also study the effects of the inter-channel coupling $ \tilde{t} $, and observe that increasing $ \tilde{t} $ reduces the delocalized phase space, shifting the transition from $ λ_1 = λ_2 = 1 $ at $ \tilde{t} = 0 $ to $ λ_1^c + λ_2^c \approx 0.5 $ at larger $ \tilde{t} $. Furthermore, the phase transition point is found to be sensitive to both $ \tilde{t} $ and the incommensurate modulation parameter $ b $. While the general phase transition behavior is preserved, subtle differences arise for different values of $ b $, indicating a dependence of the phase boundary on both parameters. Using the cost function approach, we calculate the critical potential strength $ λ_c $ and the critical exponent $ ν$, with $ ν\approx 0.5 $ for the middle of the spectrum in both symmetric and asymmetric models.

cond-mat.dis-nn↗

arXiv2025

Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model

In this study, we perform a detailed investigation into the interplay between disorder-induced electron localization and long-range hopping amplitudes within the Selective Long-Range Tight-Binding Model (SLRTB). Through numerical simulations, we analyze the electronic properties of the system, with a focus on the participation ratio (PR), entanglement entropy (EE), energy spectrum, and the ratio of level spacings ($r_n$). Our results reveal a marked distinction between negative and positive long-range hopping amplitudes, manifesting in different electronic behaviors and transitions. Notably, we carry out a finite-size scaling analysis, identifying the critical point and exponents that characterize the system's behavior near the transition. The investigation highlights the role of gapless regions in shaping the system's PR, $r_n$, and EE, and the influence of disorder on these properties. The SLRTB model proves to be an effective framework for understanding the effects of disorder and long-range hopping on electron dynamics, offering valuable insights into localization and delocalization phenomena.

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arXiv2025

Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement Measures

We investigate the directional localization properties of wave-functions in a two-dimensional tight-binding model with uniform hopping and correlated random on-site energies. By controlling the disorder correlation strength with a parameter $α$, we explore the effects of disorder on wave-function localization using Single Particle Entanglement Entropy (SPEE) and Single Particle Rényi Entropy (SPRE) at different values of $q$. Our analysis includes two distinct randomness structures: row-wise and fully correlated disorder. We find that row-wise disorder maintains maximal entanglement for horizontal cuts while enhancing horizontal spread for vertical cuts as $α$ increases. In contrast, fully correlated disorder leads to reduced vertical entanglement for horizontal cuts and increased horizontal entanglement for vertical cuts with rising $α$. Additionally, our results show that the difference between SPEE and SPRE provides valuable insights into localization behavior. These findings highlight the significance of directional properties in understanding localization transitions in disordered systems.

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arXiv2023

Exploring Entanglement Characteristics in Disordered Free Fermion Systems through Random Bi-Partitioning

This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as $EE \propto L^D$, where $D$ represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed.

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arXiv2023

Entanglement entropy of XX spin $1/2$ chain with random partitioning at arbitrary temperature

We study the entanglement properties of random XX spin $1/2$ chains at an arbitrary temperature $T$ using random partitioning, where sites of a size-varying subsystem are chosen randomly with a uniform probability $p$, and then an average over subsystem possibilities is taken. We show analytically and numerically, using the approximate method of real space renormalization group, that random partitioning entanglement entropy for the XX spin chain of size $L$ behaves like EE$(T,p) = a(T,p) L$ at an arbitrary temperature $T$ with a uniform probability $p$, i.e., it obeys volume law. We demonstrate that $a(T,p) = \ln(2) \langle P_s + P_{t_{\uparrow\downarrow}} \rangle p(1-p)$, where $P_s$ and $P_{t_{\uparrow\downarrow}}$ are the average probabilities of having singlet and triplet$_{\uparrow\downarrow}$ in the entire system, respectively. We also study the temperature dependence of pre-factor $a(T,p)$. We show that EE with random partitioning reveals both short- and long-range correlations in the entire system.

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arXiv2023

Characterizing the delocalized-localized Anderson phase transition based on the system's response to boundary conditions

A new characterization of the Anderson phase transition, based on the response of the system to the boundary conditions is introduced. We change the boundary conditions from periodic to antiperiodic and look for its effects on the eigenstate of the system. To characterize these effects, we use the overlap of the states. In particular, we numerically calculate the overlap between the ground-state of the system with periodic and antiperiodic boundary conditions in one-dimensional models with delocalized-localized phase transitions. We observe that the overlap is close to one in the localized phase, and it gets appreciably smaller in the delocalized phase. In addition, in models with mobility edges, we calculate the overlaps between single-particle eigenstate with periodic and antiperiodic boundary conditions to characterize the entire spectrum. By this single-particle overlap, we can locate the mobility edges between delocalized and localized states.

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arXiv2020

Characterizing The Many-Body Localization via Studying State Sensitivity to Boundary Conditions

We introduce novel characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to antiperiodic and calculate shift in the system's energy and shifts in the single-particle density matrix eigenvalues in the corresponding energy window. We employ the typical model for studying MBL, a one-dimensional disordered system of fermions with nearest-neighbor repulsive interaction where disorder is introduced as randomness on on-site energies. By calculating numerically the shifts in the system's energy and eigenvalues of the single-particle density matrix, we observe that in the localized regime, both shifts are vanishing; while in the extended regime, both shifts are on the order of the corresponding level spacing. We also applied these characterizations of the phase transition to the case of having next-nearest-neighbor interactions in addition to the nearest-neighbor interactions, and studied its effect on the transition.

cond-mat.str-el↗

arXiv2020

Distribution of entanglement Hamiltonian spectrum in free fermion models

We studied numerically the distribution of the entanglement Hamiltonian eigenvalues in two one-dimensional free fermion models and the typical three-dimensional Anderson model. We showed numerically that this distribution depends on the phase of the system: In the delocalized phase it is centered around very small values and in the localized phase, picks of the distribution goes to larger values. We therefore, based on the distribution of entanglement Hamiltonian eigenvalues, explain the behavior of the entanglement entropy in different phases. In addition we propose the smallest magnitude entanglement Hamiltonian eigenvalue as a characterization of phase and phase transition point (although it does not locate the phase transition point very sharply), and we verify it in the mentioned models.

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arXiv2019

Single-particle Entanglement of the Entanglement Hamiltonian Eigen-modes

Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigen-mode in a one-dimensional free fermion model that undergoes a delocalized-localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigen-mode has the same behavior as EPEE of Hamiltonian eigen-mode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decreases in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigen-mode -- which can be obtained through the calculation of moments of SPEE -- signature very sharply the phase transition point. These two modes are also compared by calculation of single particle Réyni entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigen-mode can be used as a phase detection parameter.

cond-mat.str-el↗

arXiv2019

Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models

We study entanglement Hamiltonian (EH) associated with the reduced density matrix of free fermion models in delocalized-localized Anderson phase transition. We show numerically that the structure of the EH matrix differentiates the delocalized from the localizedphase. In the delocalized phase, EH becomes a long-range Hamiltonian but is short-range in the localized phase, no matter what the configuration of the system's Hamiltonian is (whether it is long or short range). With this view, we introduce the entanglement conductance (EC), which quantifies how much EH is long-range and propose it as an alternative quantity to measure entanglement in the Anderson phase transition, by which we locate the phase transition point of some one-dimensional free fermion models; and also by applying the finite size method to the EC, we find three-dimensional Anderson phase transition critical disorder strength.

cond-mat.str-el↗

arXiv2019

Multi-fractality of the entanglement Hamiltonian eigen-modes

We study the fractal properties of single-particle eigen-modes of entanglement Hamiltonian in free fermion models. One of these modes that has the highest entanglement information and thus called maximally entangled mode (MEM) is specially considered. In free Fermion models with Anderson localization, fractality of MEM is obtained numerically and compared with the fractality of Hamiltonian eigen-mode at Fermi level. We show that both eigen-modes have similar fractal properties: both have same single fractal dimension in delocalized phase which equals the dimension of the system, and both show multi-fractality at phase transitio point. Therefore, we conclude that, fractal behavior of MEM -- in addition to the fractal behavior of Hamiltonian eigen-mode -- can be used as a quantum phase transition characterization.

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arXiv2017

Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization

Sensitivity of entanglement Hamiltonian spectrum to boundary conditions is considered as a phase detection parameter for delocalized-localized phase transition. By employing one-dimensional models that undergo delocalized-localized phase transition, we study the shift in the entanglement energies and the shift in the entanglement entropy when we change boundary conditions from periodic to anti-periodic. Specifically, we show that both these quantities show a change of several orders of magnitude at the transition point in the models considered. Therefore, this shift can be used to indicate the phase transition points in the models. We also show that both these quantities can be used to determine \emph{mobility edges} separating localized and delocalized states.

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arXiv2016

Entanglement spectrum and entangled modes of highly excited states in random XX spin chains

We examine the real space renormalization group method of finding \textit{excited eigenstate} (RSRG-X) of the XX spin-1/2 chain, from entanglement perspectives. Eigenmodes of entanglement Hamiltonian, especially the maximally entangled mode and corresponding entanglement energies are studied and compared with predictions of RSRG-X. Our numerical results demonstrate the accuracy of the RSRG-X method in the strong disorder limit, and quantify its error when applied to weak disorder regime. Overall, our results validate the RSRG-X method qualitatively, but also show that its accuracy decreases with increasing temperature.

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arXiv2015

Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

We calculate numerically the entanglement entropy of free fermion ground states in one-, two- and three-dimensional Anderson models, and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.

cond-mat.str-el↗

arXiv2015

Effect of Single Impurity on Free Fermion Entanglement Entropy

The one-dimensional free Fermi gas is a prototype conformally invariant system, whose entanglement properties are well-understood. In this work, the effects of a single impurity on one dimensional free fermion entanglement entropy are studied both analytically and numerically. Such an impurity represents an exactly marginal perturbation to the bulk conformally invariant fixed point. We find that the impurity leads to sub-leading contributions to the entanglement entropy that scale inversely with the subsystem size. The origin of such contributions are identified.

cond-mat.str-el↗

arXiv2014

Maximally Entangled Mode, Metal-Insulator Transition and Violation of Entanglement Area Law in Non-interacting Fermion Ground States

We study in this work the ground state entanglement properties of two models of non-interacting fermions moving in one-dimension (1D), that exhibit metal-insulator transitions. We find that entanglement entropy grows either logarithmically or in a power-law fashion in the metallic phase, thus violating the (1D version of) entanglement area law. No such violation is found in the insulating phase. We further find that characteristics of {\em single fermion} states at the Fermi energy (which can {\em not} be obtained from the many-fermion Slater determinant) is captured by the lowest energy single fermion mode of the {\em entanglement} Hamiltonian; this is particularly true at the metal-insulator transition point. Our results suggest entanglement is a powerful way to detect metal-insulator transitions, {\em without} knowledge of the Hamiltonian of the system.

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