arXiv subjects

Shaon Sahoo

Publications and source records attributed to Shaon Sahoo.

At least 19 recordsLinked to original sources

arXiv2026

Entangling Power Dynamics: Ergodicity and Mixing

We study quantum dynamics through the lens of entanglement generation and characterize the underlying unitary evolution by the distinct signatures it imprints on the time-dependent entangling power. For a unitary operator, we characterize ergodicity by the equality between its long-time-averaged entangling power and the Haar-averaged linear entropy. We define mixing more stringently as the convergence of the time-dependent entangling power itself to the Haar value at long times. Within this framework, we establish the ergodic hierarchy of dynamical behavior, showing in particular that mixing implies ergodicity, whereas ergodicity does not necessarily imply mixing. As an application, we find that two-qubit unitary gates are neither ergodic nor mixing: their long-time-averaged entangling power can take only four discrete values, none of which coincides with the Haar average. We then investigate many-body dynamics using the kicked Ising chain and find that the long-time-averaged entangling power converges to the Haar value in both integrable and nonintegrable cases, indicating ergodicity. Remarkably, however, the nonintegrable chain exhibits mixing, whereas the integrable chain, despite being ergodic, is demonstrably nonmixing. We also introduce a Lyapunov-like exponent to characterize the rate at which the time-dependent entangling power approaches its saturation value. We find that this exponent increases systematically with the degree of integrability breaking in the many-body system. Our results establish entanglement generation as a useful framework for characterizing dynamical systems and reveal qualitatively different signatures of integrability beyond conventional diagnostics.

quant-ph↗

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↗

arXiv2025

Quantum thermalization in a dimerized J1-J2 model

We revisit the J1-J2 frustrated Heisenberg spin-1/2 chain with dimerization ({\delta}) or modulation in the nearest-neighbor couplings to investigate its thermalization behavior. While the dimerization tends to induce localization, the next-nearest-neighbor interaction J2 generally favors thermalization, making the assessment of the model's compliance with the Eigenstate Thermalization Hypothesis (ETH) particularly subtle. The challenge is further compounded by the model's SU(2) symmetry; the study of ETH compliance is necessarily done for each symmetry sector but separating different sectors of this symmetry is known to be a computationally demanding task. The current study is driven by two main motivations: first, to explore whether the well-known ground-state phases of the model have any bearing on its thermalization properties; and second, to understand how the interplay between two competing factors, namely, the non-uniformity (via {\delta}) and the beyond-nearest-neighbor interactions (via J2) governs the system's approach to thermal equilibrium. A systematic analysis shows that the ETH is most strongly satisfied for intermediate values of {\delta} (~ 0.5) with J2 ranging from intermediate (~ 0.5) to large (~ 1)- a parameter regime falls within the spiral ground-state phase. It is also found that when the system is in the gapless ground-state phase (which falls within the N'eel phase), the ETH is more prone to violation. In the regime of large {\delta} and small J2, the system is seen to enter a localized phase (characterized here by modulation in density-of-states; assessing ETH compliance is less meaningful for this phase.

cond-mat.stat-mech↗

arXiv2025

Quantum thermalization and average entropy of a subsystem

Page's seminal result on the average von Neumann (VN) entropy does not immediately apply to realistic many-body systems which are restricted to physically relevant smaller subspaces. We investigate here the VN entropy averaged over the pure states in the subspace $\mathcal{H}_E$ corresponding to a narrow energy shell centered at energy $E$. We find that the average entropy is $\overline{S}_{1} \simeq \ln d_1$, where $d_1$ represents first subsystem's effective number of states relevant to the energy scale $E$. If $d_E = \dim{(\mathcal{H}_E)}$ and $D$ ($D_1$) is the Hilbert space dimension of the full system (first subsystem), we estimate that $d_1 \simeq D_1^\gamma$, where $\gamma = \ln (d_E) / \ln (D)$ for nonintegrable (chaotic) systems and $\gamma < \ln (d_E) / \ln (D)$ for integrable systems. This result can be reinterpreted as a volume-law of entropy, where the volume-law coefficient depends on the density-of-states for nonintegrable systems, and remains below the maximal possible value for integrable systems. We numerically analyze a spin model to substantiate our main results.

quant-ph↗

arXiv2025

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-Andr\'{e} (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-Andr\'{e} (GAA) model.

cond-mat.stat-mech↗

arXiv2024

Statistical entropy of quantum systems

Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical mechanics remain an area of active debate and are yet to be fully understood. This work is motivated by the need to develop a comprehensive understanding of the statistical measures of thermodynamic entropy in quantum systems - a topic intimately connected to the phenomenon of quantum thermalization. In particular, we investigate the conditions under which the von Neumann entropy can be regarded as a valid statistical measure of thermodynamic entropy in quantum systems. This paper demonstrates that the equivalence between the von Neumann and thermodynamic entropies is not universal, but instead depends on several subtle and often overlooked assumptions. In this context, we also briefly revisit key criticisms of von Neumann entropy - particularly its time-invariance and subadditivity - and argue that these concerns can be meaningfully addressed in the setting of thermodynamic systems. To substantiate some arguments and to clarify some issues, we provide suitable numerical results from our analysis of a spin-1/2 system.

quant-ph↗

arXiv2024

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↗

arXiv2023

On twin prime distribution and associated biases

A modified totient function ($ϕ_2$) is seen to play a significant role in the study of the twin prime distribution. The function is defined as $ϕ_2(n):=\#\{a\le n ~\vert ~\textrm{$a(a+2)$ is coprime to $n$}\}$ and is shown here to have following product form: $ϕ_2(n) = n (1-\frac{θ_n}{2}) \prod_{p>2,~p\vert n}(1-\frac 2 p)$, where $p$ denotes a prime and $θ_n = 0$ or $1$ for odd or even $n$ respectively. Using this function it is proved for a given $n$ that there always exists a number $m > n$ so that $(p, m(m + 2)) = 1$ for every prime $p \le n$. We also establish a Legendre-type formula for the twin prime counting function in the following form: $π_2(x) - π_2(\sqrt{x}) = \sum_{ab\vert P(\sqrt{x})}μ(ab) \left[\frac{x-l_{a,b}}{ab}\right]$, where $P(z)=\prod_{p\le z}p$ and $a$ is always odd. Here $l_{a,b}$ is the lowest positive integer so that $a\vert l_{a,b}$ and $b\vert (l_{a,b}+2)$. In the latter part of this work, we discussion three different types of biases in the distribution of twin primes. The first two biases are similar to the biases in primes as reported by Chebyshev, and Oliver and Soundararajan. Our third reported bias is on the difference ($D$) between (the first members of) two consecutive twin primes; it is observed that $D\pm1$ is more likely to be a prime than an odd composite number.

math.NT↗

arXiv2023

Magnetic plateaus and jumps in a spin-1/2 ladder with alternate Ising-Heisenberg rungs: a field dependent study

We study a frustrated two-leg spin-1/2 ladder with alternate Ising and isotropic Heisenberg rung exchange interactions, whereas, interactions along legs and diagonals are Ising type. The ground-state (GS) of this model has four exotic phases: (i) the stripe rung ferromagnet (SRFM), (ii) the anisotropic anti-ferromagnet (AAFM), (iii) the Dimer, and (iv) the stripe leg ferromagnet (SLFM) in absence of any external magnetic field. In this work, we study the effect of externally applied longitudinal and transverse fields on GS phases and note that there are two plateaus with per-site magnetization $1/4$ and $1/2$. There is another plateau at zero magnetization due to a finite spin gap in the presence of a longitudinal field. The exact diagonalization (ED) and the transfer matrix (TM) methods are used to solve the model Hamiltonian and the mechanism of plateau formation is analyzed using spin density, quantum fidelity, and quantum concurrence. In the (i) SRFM phase, Ising exchanges are dominant for all spins but the Heisenberg rungs are weak, and therefore, the magnetization shows a continuous transition as a function of the transverse field. In the other three phases [(ii)-(iv)], the Ising dimer rungs are weak and those are broken first to reach a plateau with per-site magnetization $1/4$, having a large gap which is closed by further application of the transverse field.

cond-mat.str-el↗

arXiv2022

On the existence of twin prime in an interval

Let $S_{(x,y]} = \left\{\frac{p_n}{p_{n+1}-2} :~ n\in I \right\}$, where $I = \left\{n :~ x 0}$. If $M_α(x,y)$ denotes the $α$-power mean of the elements of $S_{(x,y]}$, it is shown that the existence of a twin prime pair in $(x,y]$ is implied if $\displaystyle \lim_{α\rightarrow \infty}M_α(x,y) > 1 - 2/y + O(y^{-2})$ for a sufficiently large $y$. For a special choice of $y$, we also find a lower bound for the mean: $\displaystyle \lim_{α\rightarrow \infty}M_α(x,x^β)>1-c/x^β+O(x^{-β}\log^{-1} x)$, where the constant $c>0$ and $β= 1+c/\log^2 x$ or equivalently, $x^β=x+cx/\log x+O(x/\log^2 x)$. With $c<2$, the lower bound for $\displaystyle \lim_{α\rightarrow \infty}M_α(x,x^β)$ satisfies the inequality on the existence of a twin prime in the interval $(x,x^β]$.

math.GM↗

arXiv2020

Ground state properties and exact thermodynamics of a 2-leg anisotropic spin ladder system

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either $S$ or $σ$-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both $S$ and $σ$-type of spins are anti-ferromagnetically aligned with each other, two nearest $S$ spins along the rung form an anisotropic singlet bond whereas two nearest $σ$ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like $Cv(T)$, $χ(T)$ and $S(T)$ are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from $χ(T)$ and $Cv(T)$ curves.

cond-mat.str-el↗

arXiv2020

Haldane and Dimer phases in a frustrated spin chain: an exact groundstate and associated topological phase transition

A Heisenberg spin-$s$ chain with alternating ferromagnetic ($-J_1^F<0$) and antiferromagnetic ($J_1^A>0$) nearest-neighbor (NN) interactions, exhibits the Dimer and spin-$2s$ Haldane phases in the limits $J_1^F/J_1^A \rightarrow 0$ and $J_1^F/J_1^A \rightarrow \infty$ respectively. These two phases are understood to be topologically equivalent. Induction of the frustration through the next nearest-neighbor ferromagnetic interaction ($-J_2^F<0$) produces a very rich quantum phase diagram. With frustration, the whole phase diagram is divided into a ferromagnetic (FM) and a nonmagnetic (NM) phase. For $s=1/2$, the full NM phase is seen to be of Haldane-Dimer type, but for $s>1/2$, a spiral phase comes between the FM and the Haldane-Dimer phases. The study of a suitably defined string-order parameter and spin-gap at the phase boundary indicates that the Haldane-Dimer and spiral phases have different topological characters. We also find that, along the $J_2^F=\frac 12 J_1^F$ line in the NM phase, an NN dimer state is the {\it exact} groundstate, provided $J_1^A>J_C=κJ_1^F$ where $κ\le s + h$ for applied magnetic field $h$. Without magnetic field, the position of $J_C$ is on the FM-NM phase boundary when $s=1/2$, but for $s>1/2$, the location of $J_C$ is on the phase separation line between the Haldane-Dimer and spiral phases.

cond-mat.str-el↗

arXiv2019

Periodically Driven Many-Body Systems: A Floquet Density Matrix Renormalization Group Study

Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the potential to uncover a whole field of new phenomena, but the theoretical and numerical understanding becomes extremely difficult. We now propose a promising numerical method by generalizing the density matrix renormalization group to a superposition of Fourier components of periodically driven many-body systems using Floquet theory. With this method we can study the full time-dependent quantum solution in a large parameter range for all evolution times, beyond the commonly used high-frequency approximations. Numerical results are presented for the isotropic Heisenberg antiferromagnetic spin-1/2 chain under both local(edge) and global driving for spin-spin correlations and temporal fluctuations. As the frequency is lowered, we demonstrate that more and more Fourier components become relevant and determine strong length- and frequency-dependent changes of the quantum correlations that cannot be described by effective static models.

cond-mat.str-el↗

arXiv2017

Out-of-equilibrium Kondo Effect in a Quantum Dot: Interplay of Magnetic Field and Spin Accumulation

We present a theoretical study of low temperature nonequilibrium transport through an interacting quantum dot in the presence of Zeeman magnetic field and current injection into one of its leads. By using a self-consistent renormalized equation of motion approach, we show that the injection of a spin-polarized current leads to a modulation of the Zeeman splitting of the Kondo peak in the differential conductance. We find that an appropriate amount of spin accumulation in the lead can restore the Kondo peak by compensating the splitting due to magnetic field. By contrast when the injected current is spin-unpolarized, we establish that both Zeeman-split Kondo peaks are equally shifted and the splitting remains unchanged. Our results quantitatively explain the experimental findings reported in KOBAYASHI T. et al., Phys. Rev. Lett. 104, 036804 (2010). These features could be nicely exploited for the control and manipulation of spin in nanoelectronic and spintronic devices.

cond-mat.mes-hall↗

arXiv2016

Analyzing research performance: proposition of a new complementary index

A researcher collaborating with many groups will normally have more papers (and thus higher citations and $h$-index) than a researcher spending all his/her time working alone or in a small group. While analyzing an author's research merit, it is therefore not enough to consider only the collective impact of the published papers, it is also necessary to quantify his/her share in the impact. For this quantification, here I propose the $I$-index which is defined as an author's percentage share in the total citations that his/her papers have attracted. It is argued that this $I$-index does not directly depend on the most of the subjective issues like an author's influence, affiliation, seniority or career break. A simple application of the Central Limit Theorem shows that, the scheme of equidistribution of credit among the coauthors of a paper will give us the most probable value of the $I$-index (with an associated small standard deviation which decreases with increasing $h$-index). I show that the total citations ($N_c$), the $h$-index and the $I$-index are three independent parameters (within their bounds), and together they give a comprehensive idea of an author's overall research performance.

cs.DL↗

arXiv2015

Optimal linear Glauber model

Contrary to the actual nonlinear Glauber model (NLGM), the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate ($w_j$) in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear $w_j$ are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau (TDGL) equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

cond-mat.stat-mech↗

arXiv2014

Optimal values of bipartite entanglement in a tripartite system

For a general tripartite system in some pure state, an observer possessing any two parts will see them in a mixed state. By the consequence of Hughston-Jozsa-Wootters theorem, each basis set of local measurement on the third part will correspond to a particular decomposition of the bipartite mixed state into a weighted sum of pure states. It is possible to associate an average bipartite entanglement ($\bar{\mathcal{S}}$) with each of these decompositions. The maximum value of $\bar{\mathcal{S}}$ is called the entanglement of assistance ($E_A$) while the minimum value is called the entanglement of formation ($E_F$). An appropriate choice of the basis set of local measurement will correspond to an optimal value of $\bar{\mathcal{S}}$; we find here a generic optimality condition for the choice of the basis set. In the present context, we analyze the tripartite states $W$ and $GHZ$ and show how they are fundamentally different.

quant-ph↗

arXiv2014

Studies on a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic exchanges

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic ($J_1^F$) and antiferromagnetic ($J_1^A$) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction ($J_2^F$). In this model frustration is present due to the non-zero $J_2^F$. The model with site spin $s$ behaves like a Haldane spin chain with site spin 2$s$ in the limit of vanishing $J_2^F$ and large $J_1^F/J_1^A$. We show that the exact ground state of the model can be found along a line in the parameter space. For fixed $J_1^F$, the phase diagram in the space of $J_1^A-J_2^F$ is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

cond-mat.str-el↗