arXiv subjects

Saptarshi Mandal

Publications and source records attributed to Saptarshi Mandal.

At least 37 records · Page 2Linked to original sources

arXiv2023

Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part I -- static properties

Recently, the Kitaev-Heisenberg-$\Gamma$ system has been used to explore various aspects of Kitaev spin liquid physics. Here, we consider a few small clusters of up to twelve sites and study them in detail to unravel many interesting findings due to the competition between all possible signs and various magnitudes of these interactions under the influence of an external magnetic field. When Heisenberg interaction is taken anti-ferromagnetic, one obtains plateaus in correlation functions where, surprisingly, the exact groundstate reduces to the eigenstate of Heisenberg interaction as well. On the other hand, for ferromagnetic Heisenberg interaction, its competition with Kitaev interaction results in non-monotonicity in the correlation functions. We discuss, in detail, the competing effects on low energy spectrum, flux operator, magnetization, susceptibility, and specific heat. Finally, we discuss how our findings could be helpful to explain some of the recent experimental and theoretical findings in materials with Kitaev interactions.

cond-mat.str-el↗

arXiv2023

Topological characterization of special edge modes from the winding of relative phase

The symmetry-constrained topological invariant fails to explain the emergence of the special edge modes when system does not preserve discrete symmetries. The inversion or chiral symmetry broken SSH model is an example of one such system where one-sided edge state with finite energy appears at one end of the open chain. To investigate whether this special edge mode is of topological origin or not, we introduce a concept of relative phase between the components of a two-component spinor and define a winding number by the change of this relative phase over the one-dimensional Brillouin zone. The relative phase winds non-trivially (trivially) in accord with the presence (absence) of the one-sided edge mode inferring the bulk boundary correspondence. We extend this analysis to a two dimensional case where we characterize the non-trivial phase, hosting gapped one-sided edge mode, by the winding in relative phase only along a certain axis in the Brillouin zone. We demonstrate all the above findings from a generic parametric representation while topology is essentially determined by whether the underlying lower-dimensional projection includes or excludes the origin. Our study thus reveals a new paradigm of symmetry broken topological phases for future studies.

cond-mat.mes-hall↗

arXiv2023

Spectral Clustering for Crowdsourcing with Inherently Distinct Task Types

The Dawid-Skene model is the most widely assumed model in the analysis of crowdsourcing algorithms that estimate ground-truth labels from noisy worker responses. In this work, we are motivated by crowdsourcing applications where workers have distinct skill sets and their accuracy additionally depends on a task's type. While weighted majority vote (WMV) with a single weight vector for each worker achieves the optimal label estimation error in the Dawid-Skene model, we show that different weights for different types are necessary for a multi-type model. Focusing on the case where there are two types of tasks, we propose a spectral method to partition tasks into two groups that cluster tasks by type. Our analysis reveals that task types can be perfectly recovered if the number of workers $n$ scales logarithmically with the number of tasks $d$. Any algorithm designed for the Dawid-Skene model can then be applied independently to each type to infer the labels. Numerical experiments show how clustering tasks by type before estimating ground-truth labels enhances the performance of crowdsourcing algorithms in practical applications.

cs.LG↗

arXiv2022

Projective symmetry group classification of Abrikosov fermion mean-field ans\"atze on the square-octagon lattice

We perform a projective symmetry group (PSG) classification of symmetric quantum spin liquids with different gauge groups on the square-octagon lattice. Employing the Abrikosov fermion representation for spin-$1/2$, we obtain $32$ $SU(2)$, $1808$ $U(1)$ and $384$ $\mathbb{Z}_{2}$ algebraic PSGs. Constraining ourselves to mean-field parton ans\"atze with short-range amplitudes, the classification reduces to a limited number, with 4 $SU(2)$, 24 $U(1)$ and 36 $\mathbb{Z}_{2}$, distinct phases. We discuss their ground state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.

cond-mat.str-el↗

arXiv2022

Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator

In this work, we study the time-dependent behaviour of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger-Keldysh formalism in presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstates and continuous energy eigenvalues. Using the expression for the eigenstates, we further derive the most general expression for the generating function as well as the out-of-time-ordered correlators (OTOC) for the given system using this formalism. Further, considering the time-dependent coupling and frequency of the quantum inverted oscillator characterized by quench parameters, we comment on the dynamical behaviour, specifically the early, intermediate and late time-dependent features of the OTOC for the quenched quantum inverted oscillator. Next, we study a specific case, where the system of inverted oscillator exhibits chaotic behaviour by computing the quantum Lyapunov exponent from the time-dependent behaviour of OTOC in presence of the given quench profile.

hep-th↗

arXiv2022

Circuit Complexity in an interacting quenched Quantum Field Theory

In this work, we explore the effects of a quantum quench on the circuit complexity for a quenched quantum field theory having weakly coupled quartic interaction. We use the invariant operator method, under a perturbative framework, for computing the ground state of this system}. We give the analytical expressions for specific reference and target states using the ground state of the system. Using a particular cost functional, we show the analytical computation of circuit complexity for the quenched and interacting field theory. Further, we give a numerical estimate of circuit complexity with respect to the quench rate, $\delta t$ for two coupled oscillators. The parametric variation of the unambiguous contribution of the circuit complexity for an arbitrary number of oscillators has been studied with respect to the dimensionless parameter $(t/\delta t$). We comment on the variation of circuit complexity for different values of coupling strength, different number of oscillators, and even in different dimensions.

hep-th↗

arXiv2022

Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model

The higher-order corner modes for quantum anomalous Hall insulators in $C_3$ symmetry broken honeycomb lattice have been engineered recently. Here we consider an extended Haldane model in presence of inversion symmetry breaking sub-lattice mass, time-reversal symmetry breaking Zeeman field and spin-orbit coupling interaction where we find that only the quantum spin Hall insulator can host the second-order dipolar phase while the remaining two first-order topological phases do not morph into the latter. Remarkably, four-fold degeneracy of zero-energy dipolar states can be reduced to two-fold under the application (withdrawn) of sub-lattice mass (Zeeman field) term when the spin-orbit coupling is already present. On the other hand, the sub-lattice mass and Zeeman field terms compete with each other to pin down the two mid-gap states at zero-energy in the absence or presence of spin-orbit coupling. Interestingly, the bulk-polarization can topologically characterize the dipolar phase irrespective of the energy of the mid-gap states as long as inversion symmetry is preserved. The effective gap criterion can qualitatively mimic the extent of SOT phase originated by the interplay between finite Zeeman exchange field, sub-lattice mass, and SOC interaction.

cond-mat.mes-hall↗

arXiv2022

Entanglement in interacting quenched two-body coupled oscillator system

In this work, we explore the effects of a quantum quench on the entanglement measures of a two-body coupled oscillator system having quartic interaction. We use the invariant operator method, under a perturbative framework, for computing the ground state of this system. We give the analytical expressions for the total and reduced density matrix of the system having non-Gaussian, quartic interaction terms. Using this reduced density matrix, we show the analytical calculation of two entanglement measures viz., Von Neumann entanglement entropy using replica trick and Renyi entanglement entropy. Further, we give a numerical estimate of these entanglement measures with respect to the dimensionless parameter $(t/\delta t$) and show its behaviour in the three regimes, i.e; late time behaviour, around the quench point and the early time behaviour. We comment on the variation of these entanglement measures for different orders of coupling strength. The variation of Renyi entropy of different orders has also been discussed.

hep-th↗

arXiv2021

Circuit Complexity in $\mathcal{Z}_{2}$ ${\cal EEFT}$

Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in $\mathcal{Z}_2$ Even Effective Field Theories ($\mathcal{Z}_2$ EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as $\phi^{4}$, $\phi^{6}$ and $\phi^8.$ To facilitate our computation we regularize the theory by putting it on a lattice. First, we consider a simple case of two oscillators and later generalize the results to $N$ oscillators. The study has been carried out for nearly Gaussian states. In our computation, the reference state is an approximately Gaussian unentangled state, and the corresponding target state, calculated from our theory, is an approximately Gaussian entangled state. We compute the complexity using the geometric approach developed by Nielsen, parameterizing the path ordered unitary transformation and minimizing the geodesic in the space of unitaries. The contribution of higher-order operators, to the circuit complexity, in our theory has been discussed. We also explore the dependency of complexity with other parameters in our theory for various cases.

hep-th↗

arXiv2021

Interference Effect of Beam Splitter Current in Iron-Pnictide Superconductors

We consider a Cooper pair beam splitter for Iron-Pnictide superconductor and calculate the entangled electron-hole current. We investigate the interplay of various physical parameters such as doping at electron and hole pockets as well as non-zero nesting between the electron and hole pocket. We find that in the absence of magnetic order, the current due to hole pocket and electron pocket add up ordinarily. However in the presence of magnetic ordering the two currents take part in characteristic interference effect to modify the resultant current significantly. This interference effect manifests itself in non-monotonous and oscillatory nature of beam splitter current. We investigate in details this non-monotonicity with the chemical potential as well as nesting vectror $|\bf q|$. We also investigate the evolution of density of states with system parameters and correlate it with the beam-splitter current. Further we enumerate the relevant parameter space where the efficiency of such beam splitter set up is enhanced. Our finding can be useful in experimental determination or verification of co-existence phase in Iron-Pnictide superconductors and has potential applications in realizing quantum gates or switches.

cond-mat.supr-con↗

arXiv2021

Eight fold quantum Hall phases in a time reversal symmetry broken tight binding model

We consider a time reversal symmetry (TRS) broken Kane-Mele model superimposed with Haldane model and chart out the phase diagram using spin Chern number to investigate the fate of quantum anomalous Hall insulator (QAHI) and quantum spin Hall insulator (QSHI) phases. Interestingly, in addition to QSHI and QAHI phase, the phase diagram unveils quantum anomalous spin Hall insulator (QASHI) phase where only one spin sector is topological. We also find multicritical points where three / four topological phase boundaries coalesce. These topological phases are protected by an effective TRS and a composite anti-unitary particle-hole symmetry leading to remarkable properties of edge modes. We find spin-selective, spin-polarized and spin-neutral edge transport in QASHI, QSHI and QAHI phases respectively. Our study indicates that the robustness of the topological phase mainly depends on the spin gap which does not necessarily vanish at the Dirac points across a topological phase transition. We believe that our proposals can be tested in near future using recent experimental advancements in solid state and cold atomic systems.

cond-mat.mes-hall↗

arXiv2021

Ground state many-body quantum entanglement of frustrated transverse field models on square lattice

We study the ground state (GS) many-body quantum entanglement of two different transverse field models on a quasi-2D square lattice relevant to a Hydrogen-bonded crystal, i.e, squaric acid. We measure the genuine multipartite qubit-entanglement ($C_{\text{GME}}(\psi)$) of the ground state of very generic models with all the possible cases of exchange couplings considered under defect free and one lattice site defect conditions. Our results show that creation, decay of multipartite entanglement occur for different combinations of coupling strength. When frustration is maximum the system exhibits a peak in concurrence after a gradual increase from disentangled state at zero field followed by an asymptotic decay at large fields. In contrast, for a marginally frustrated (degenerate) case though the concurrence shows a peak, the entanglement is non-zero and large at zero fields. Our results discuss the sensitivity of the qubit-entanglement with underlying GS of varying degree of degeneracy. We conclude that despite of their similarities in ground state properties, yet we see a difference in the degree of entanglement between the two models. We conjecture this result could be due to the difference in the amount of degeneracy and the quantum ground states of both Hamiltonians that could dictate the results even in the thermodynamic limit.

cond-mat.str-el↗

arXiv2020

Competing orders in a frustrated Heisenberg model on the Fisher lattice

We investigate the Heisenberg model on a decorated square (Fisher) lattice in the presence of first-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange couplings, with antiferromagnetic $J_{1}$. The classical ground-state phase diagram obtained within a Luttinger-Tisza framework is spanned by two antiferromagnetically ordered phases, and an infinitely degenerate antiferromagnetic chain phase. Employing classical Monte Carlo simulations we show that thermal fluctuations fail to lift the degeneracy of the antiferromagnetic chain phase. Interestingly, the spin-wave spectrum of the N\'eel state displays three Dirac nodal loops out of which two are symmetry protected while for the antiferromagnetic chain phase we find symmetry-protected Dirac lines. Furthermore, we investigate the spin $S=\frac{1}{2}$ limit employing a bond operator formalism which captures the singlet-triplet dynamics, and find a rich ground-state phase diagram host to a variety of valence bond solid orders in addition to antiferromagnetically ordered phases.

cond-mat.str-el↗

arXiv2020

An introduction to Kitaev model-I

This pedagogical article is aimed to the beginning graduate students interested in broad field of frustrated magnetism. We introduce and present some of the exact results obtained in Kitaev model. The Kitaev model embodies an unusual two spin interactions yet exactly solvable model in two dimension. This exact solvability renders it to realize many emergent many body phenomena such as $Z_2$ gauge field, spin liquid states, spin fractionalization, topological order exactly. First we present the exact solution of Kitaev model using Majorana fermionisation and elaborate in detail the $Z_2$ gauge structure. Following this we discuss exact calculation of magnetization, spin-spin correlation function establishing its spin-liquid character. Spin fractionalization and de-confinement of Majorana fermion is explained in detail. Existence of long range multi-spin correlation function and topological degeneracy are discussed to elucidate the entangled and topological nature of any eigenstate. Some elementary questionnaires are provided in appropriate places for assimilation of the technical details.

cond-mat.str-el↗

arXiv2019

Existence of nodal line semi-metal in a generalized three dimensional Haldane model

We construct and study a time reversal broken tight binding model on diamond lattice with complex next-nearest-neighbour hopping which can be thought of as a generalisation of two dimensional Haldane model in three dimension. The model also breaks inversion symmetry owing to sub-lattice dependent chemical potential. We calculate the spectrum of the model and find the existence of six pairs of anisotropic gapless points with linear dependence on momentum. The coordinates of the gapless points are ($2 \pi, \pi \pm k_0,0),~ (2 \pi, \pi \pm k_0,2 \pi)$ and their possible permutations . The condition for gapless spectrum is very similar to the two dimensional case. Each gapless points are having well defined chirality and in the gapless phase specific set of planes have non-zero Chern number. The gapped phase is a trivial bulk insulator which has vanishing Chern number as well as Hopf index. The model belongs to the symmetry class AIII according to the ten-fold way of classification. Surprisingly the gapless phase does contain a gapped surface state where as the gapped state has a gapless surface states as found in (1,1,1) direction.

cond-mat.str-el↗

arXiv2019

Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field

We have studied the revival of Hofstadter butterfly due to the competition between disorder and electronic interaction using mean field approximation of unrestricted Hartree Fock method at zero temperature for two dimensional square and honeycomb lattices. Interplay of disorder and electronic correlation to nullify each other is corroborated by the fact that honeycomb lattice needs more strength of electronic correlation owing to its less co-ordination number which enhances the effect of disorder. The extent of revival of the butterfly is better in square than honeycomb lattice due to higher coordination number. The effect of disorder and interaction is also investigated to study entanglement entropy and entanglement spectrum. It has been observed that for the square lattice, area law of entanglement entropy is violated for intermediate strength magnetic and magnitude of such departure from area law depends on disorder and interaction as well. However such departure from area law is absence for honeycomb lattice. Moreover the entanglement spectrum for square lattice does have the symmetry of original Hofstadter butterfly and this symmetry is destroyed in the presence of disorder. The interaction opens up a gap in the entanglement spectrum as well. For the honeycomb lattice, the entanglement spectrum forms a continuous band without any symmetry and its feature is mostly unchanged in the presence of disorder as well as interaction.

cond-mat.str-el↗

arXiv2019

Dipole-dipole interaction induced phases in Hydrogen-bonded squaric acid crystal

We study analytically the finite-temperature phase diagram of proton ordering of a quasi-two dimensional hydrogen-bonded system, namely the squaric acid crystal($\text{H}_2\text{C}_4\text{O}_4$). We take into account the four-spin interaction model at the zeroth order. Using an improvised loop algorithm within the Stochastic series expansion quantum monte carlo method, we find two distinct phases as we increase the temperature and magnetic-field. One of the phase is the $\Pi_f$, the phase with long range ferroelectric order and the other being an intermediate state with strong local correlations, i.e, a quantum liquid-like state $\Pi_{ql}$. The transition to $\Pi_{f}$ shows a very small anomalous peak in the specific heat with strong dependence of critical temperature on the strength of dipole-dipole interaction. The presence of the small peak is attributed to the absence of macroscopic degeneracy in the presence of dipole-dipole interaction and re-entrance of such degeneracy to some extent at small temperature. Though the degenerate ground state manifold is identical for a four-spin interaction or appropriate two-spin interaction model at zeroth order, we find that for the former case, the required strength of dipole-dipole interaction is quite larger to induce a ferroelectric phase. The work also presents an intricate connection of quantum fluctuation and thermal fluctuation in the presence of competing interaction with entropic effects.

cond-mat.str-el↗

arXiv2018

Defect production and quench dynamics in the three-dimensional Kitaev model

We study the quench dynamics of the three-dimensional Kitaev (spin) model under a linear drive using both exact numerical calculations and analytical "independent crossing approximation". Unlike the two-dimensional Kitaev model, the three-dimensional Kitaev model reduces to a multilevel Landau-Zener problem for each momentum. We show that for the slow quench, the defect density is proportional to the quench rate $1/\tau$. We find that the zeros of the relevant coupling between the levels determine the non-adiabatic condition for the production of defects. The contour on which the energy spectrum becomes gapless does not play an active role. The asymptotic behavior of the defect density crucially depends on the way the system reaches the non-adiabatic regime during the quenching process. We analytically show that defect correlation varies as $\tau^{-1} e^{-A/\tau}$, where $A$ is a constant independent of $\tau$. For the slow quench, the qualitative dependence of the entropy (produced during the quenching process) on the quench time is the same as that of the defect correlation, indicating a close connection between the defect correlation and the entropy content of the final state. Possible experimental realization of such quench dynamics is also described briefly.

cond-mat.str-el↗