arXiv subjects

Sujit Sarkar

Publications and source records attributed to Sujit Sarkar.

At least 19 recordsLinked to original sources

arXiv2025

Integrable Floquet Time Crystals in One Dimension

We demonstrate the realization of a Discrete Time-Crystal (DTC) phase in a family of periodically driven, one-dimensional quadratic lattice Hamiltonians that can be obtained using spin chains. These interactions preserve integrability while opening controllable gaps at resonant quasienergies and pinning the emergent quasienergy modes that are responsible for subharmonics. We demonstrate that the DTC phase is rigid in the parameter space of transverse field and an additional interaction like Next-Nearest-Neighbor (NNN) coupling strength, with the drive frequency optimized to produce the strongest subharmonic response. We also provide a detailed phase diagram of the model, exhibiting a Floquet Paramagnet (FPM) phase, as well as sharp quantum phase transitions between the FPM and the DTC. Finite-size scaling of the Floquet quasienergy splitting between the emergent subharmonic mode and its conjugate shows that the DTC lifetime diverges exponentially with system size. Thus, our work establishes a novel mechanism for achieving robust long-lived DTCs in one dimension. Motivation for this work stems from the limitations of disorder-based stabilization schemes that rely on many-body localization and exhibit only prethermal or finite-lived plateaus, eventually restoring ergodicity. Disorder-free routes are therefore highly desirable. Integrable (or Floquet-integrable) systems provide an attractive alternative because their extensive set of conserved quantities and constrained scattering strongly restrict thermalization channels. Our construction exploits these integrable restrictions together with longer-range NNN engineering to produce a clean, robust DTC that avoids the prethermal fragility of disordered realizations.

cond-mat.str-el↗

arXiv2025

Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward

Topological phases in one-dimensional superconducting systems are commonly characterized by symmetry-protected invariants. These invariants determine the number of Majorana zero-energy boundary modes but do not specify their corresponding spatial structure. In this work, we present an analytical study of Majorana zero modes (MZMs) in an extended Kitaev chain with nearest- and next-nearest-neighbor couplings. By expressing the Hamiltonian in the Majorana basis, we derive a recursion relation whose characteristic roots completely determine the spatial structure of the zero modes and yield closed-form expressions for their amplitudes. We show that, even within a single topological phase, the MZMs can exhibit qualitatively distinct decay behaviors - monotonic decay, oscillatory decay, and perfectly localized states. Remarkably, boundary-origin MZMs need not have their maximum probability at the edge of the chain. They can instead exhibit maxima at interior lattice sites with an exponentially decaying envelope from either side of the maxima. Furthermore, the characteristic roots determine the length scale required for finite chains to reproduce the semi-infinite MZM structure, providing a direct link between Hamiltonian parameters, finite-size effects, and experimentally observable spatial profiles.

cond-mat.other↗

arXiv2023

Unconventional quantum criticality in a non-Hermitian extended Kitaev chain

We investigate the nature of quantum criticality and topological phase transitions near the critical lines obtained for the extended Kitaev chain with next nearest neighbor hopping parameters and non-Hermitian chemical potential. We surprisingly find multiple gap-less points, the locations of which in the momentum space can change along the critical line unlike the Hermitian counterpart. The interesting simultaneous occurrences of vanishing and sign flipping behavior by real and imaginary components, respectively of the lowest excitation is observed near the topological phase transition. Introduction of non- Hermitian factor leads to an isolated critical point instead of a critical line and hence, reduced number of multi-critical points as compared to the Hermitian case. The critical exponents obtained for the multi-critical and critical points show a very distinct behavior from the Hermitian case.

cond-mat.str-el↗

arXiv2022

Multi-criticality and long-range effects in non-Hermitian topological models

Long-range effects induce some interesting behavior and considered as a gateway to understand the non-local behavior in the quantum systems. Especially, the long-range topological models became a platform for the realization of new quasi-particles, which are believed to be potential candidates for the topological qubits. In this work, we consider non-Hermitian Su-Schriffer-Heeger (SSH) model and discuss the interplay of non-Hermiticity and long-range effects. We use the approach of momentum space characterization, critical exponents and curvature renormalization group (CRG) method to understand the aspects of interplay. The longer-range (finite neighbors) effect produces higher winding numbers, where we observe a staircase of transitions among the even-even and odd-odd winding numbers which depends on the number of interacting neighbors. Here we also highlight the effect of multi-criticality in the system and show that they belong to a different universality class. The interplay of long-range (infinite neighbors) effect and non-Hermiticity produces fractional topological invariants, and we analyze them from the behavior of pseudo-spin vectors. We also determine the long-range and short-range limit of the model through universality class of critical exponents. Our work mainly showcases that how the study of criticality in topological system is interesting in exploring the interplay of non-Hermiticity and long-range effects.

cond-mat.str-el↗

arXiv2022

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry (non-HS) in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-HS critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-HS criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-HS critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents, and correlation function of Wannier states enable the characterization of non-HS criticalities along with multicriticalities.

cond-mat.str-el↗

arXiv2021

Physics of emergence beyond Berezinskii-Kosterlitz-Thouless transition for interacting topological quantum matter

An attempt is made to find different emergent quantum phases for interacting topological state of quantum matter. Our study is based on the quantum field theoretical renormalization group (RG) calculations. The behaviour of the RG flow lines gives the emergence of different quantum phases for non-interacting and interacting topological state of quantum matter. We show explicitly electron-electron interaction can turn a topologically trivial phase into a non-trivial one and also topological non-trivial phase to topological trivial phase. We show that physics of emergent is go beyond the quantum Berezinskii-Kosterlitz-Thouless transition. We also present the analysis of fixed point and show the behaviour of fixed point changes in presence and absence of interaction. This work provides a new perspective not only from the topological state of interacting quantum matter and but also for the correlated quantum many body physics.

cond-mat.str-el↗

arXiv2021

Signatures of topological phase transition on a quantum critical line

Recently topological states of matter have witnessed a new physical phenomenon where both edge modes and gapless bulk coexist at topological quantum criticality. The presence and absence of edge modes on a critical line can lead to an unusual class of topological phase transition between the topological and non-topological critical phases. We explore the existence of this new class of topological phase transitions in a generic model representing the topological insulators and superconductors and we show that such transition occurs at a multicritical point i.e. at the intersection of two critical lines. To characterize these transitions we reconstruct the theoretical frameworks which include bound state solution of the Dirac equation, winding number, correlation factors and scaling theory of the curvature function to work for the criticality. Critical exponents and scaling laws are discussed to distinguish between the multicritical points which separate the critical phases. Entanglement entropy and its scaling in the real-space provide further insights into the unique transition at criticality revealing the interplay between fixed point and critical point at the multicriticalities.

cond-mat.str-el↗

arXiv2021

A Quantum Field Theoretical Study of Correlated Quantum Ising model with Longer Range Interaction

The physics of quantum Ising model (qIm) plays an important role in quantum many body system. We study and present the results of qIm and longer range quantum Ising model (lqIm) in presence of strong correlation. We do the quantum field theoretical renormalization group (RG) calculation to study the behaviour of RG flow lines for different couplings for different region of parameter space. We show how the strong correlation effect enrich the quantum physics of these two systems. We show explicitly that the ordered ferromagnetic (FM) phase to the disorder quantum paramagnet (dqpI) quantum phase transition occurs for only in the strongly correlated regime for qIm and the dqpI phase appears for non-interacting and attractive regime. We show explicitly for lqIm that FM to dqpI transition occurs at the extremely correlated region and also the dqpI phase appears in correlated regime. We show that short range FM coupling and longer range coupling are competiting with each other and also the effect of strong correlation in this competition. We also show the most interesting feature that the transverse field oppose the FM coupling of qIm but it is favour the longer range coupling of lqIm. We find the evidence of another disorder quantum paramagnetic (dqpII) phase due to the relevance of longer range coupling. We also present the existence of another quantum phase transition from dqpII phase to FM phase. We show explicitly that there is no phase transition from dqpI phase to dqpII phase rather they coexists. This work provides a new perspective not only for the statistical physics of quantum Ising model but also for the quantum many body systems.

cond-mat.mes-hall↗

arXiv2021

Topological Quantum Criticality in non-Hermitian Kitaev chain with Longer Range Interaction

An Attempt is made to study the non-Hermitian effect on the topological quantum criticality and also in the physics of Majroana zero mode (MZMs). In this work, the effects and modifications done by the non-Hermitian factor $γ$ on the topological phases, criticality and also in the MZMs is studied. We use the zero mode solutions (ZMS) to construct the phase diagram. We find a correspondence between Hermitian and non-Hermitian model Hamiltonian. The MZMs appear at criticality and has a stability dependence on the new passage created because of the introduction of non-Hermiticity. The multicritical points are also studied to understand their nature under the influence of non-Hemiticity. We also study the effect of non-Hermiticity on the topological phases.

cond-mat.str-el↗

arXiv2021

Topological quantum phase transitions and criticality in a longer-range Kitaev chain

In an attempt to theoretically investigate the quantum phase transition and criticality in topological models, we study Kitaev chain with longer-range couplings (finite number of neighbors) as well as truly long-range couplings (infinite number of neighbors). We carry out an extensive topological characterization of the momentum space to explore the possibility of obtaining higher order winding numbers and analyze the nature of their stability in the model. The occurrences of phase transitions from even-to-even and odd-to-odd winding numbers are observed with decreasing longer-rangeness in the system. We derive topological quantum critical lines and study them to understand the behavior of criticality. A suppression of higher order winding numbers is observed with decreasing longer-rangeness in the model. We show that the mechanism behind such phenomena is due to the superposition and vanishing of the topological quantum critical lines associated with the higher winding number. Through the study of Berry connection we show the possible different behaviors of critical lines when they undergo superposition along with the corresponding critical exponents. We analyze the behavior of the long-range models through the momentum space characterization. We also provide exact solution for the problem and discuss the experimental aspects of the work.

cond-mat.str-el↗

arXiv2021

A Study of Curvature Theory for Different Symmetry Classes of Hamiltonian

We study and present the results of curvature for different symmetry classes (BDI, AIII and A) model Hamiltonians and also present the transformation of model Hamiltonian from one distinct symmetry class to other based on the curvature property. We observe the mirror symmetric curvature for the Hamiltonian with BDI symmetry class but there is no evidence of such behavior for Hamiltonians of AIII symmetry class. We show the origin of torsion and its consequences on the parameter space of topological phase of the system. We find the evidence of torsion for the Hamiltonian of A symmetry class. We present Serret-Frenet equations for all model Hamiltonians in $\mathbf{R}^3$ space. To the best of our knowledge, this is the first application of curvature theory to the model Hamiltonian of different symmetry classes which belong to the topological state of matter.

cond-mat.other↗

arXiv2021

Majorana Zero Modes and Bulk-Boundary Correspondence at Quantum Criticality

Majorana zero modes are well studied in the gapped phases of topological systems. We investigate Majorana zero modes at the topological quantum criticality in one dimensional topological superconducting model with longer range interaction. We identify stable localized Majorana zero modes appearing at criticality under certain conditions. Topological invariant number for these non-trivial criticalities is obtained from zeros of a complex function associated with the Hamiltonian. Behavior of parametric curve at criticalities validate the invariant obtained and account for the appearance of Majorana zero modes at criticality. Trivial and non-trivial topological nature of criticality due to the presence of multicritical point cause an unusual topological transition along the critical line. We observe and investigate this unique transition in terms of eigenvalue spectrum. Appearance of MZMs at criticality demands integer value of topological invariant number in order to validate the concept of bulk-boundary correspondence. Hence we propose a scheme to separate the invariant number into fractional and integer contribution to establish bulk-boundary correspondence at criticality.

cond-mat.str-el↗

arXiv2021

Multi-critical topological transition at quantum criticality

The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.

cond-mat.str-el↗

arXiv2020

A study of topological characterization and symmetries for a quantum simulated Kitaev chain

An attempt is made to quantum simulate the topological classification, such as winding number, geometric phase and symmetry properties for a quantum simulated Kitaev chain. We find, α (ratio between the spin-orbit coupling and magnetic field) and the range of momentum space of consideration, which plays a crucial role for the topological classification. We show explicitly that the topological quantum phase transition does not occurs at k = 0 limit for the quantum simulated Kitaev chain. We observe that the quasi-particle mass of the Majorana mode plays the significant role in topological quantum phase transition. We also show that the symmetry properties of simulated Kitaev chain is the same with original Kitaev chain. The exact solution of simulated Kitaev chain is given. This work provides a new perspective on new emerging quantum simulator and also for the topological state of matter.

cond-mat.str-el↗

arXiv2020

Quantum Berezinskii-Kosterltz-Thouless Transition for Topological Insulator

We consider the interacting helical liquid system at the one-dimensional edge of a two-dimensional topological insulator, coupled to an external magnetic field and s-wave superconductor and map it to an XYZ spin chain system. This model undergoes quantum Berezinskii-Kosterlitz-Thouless (BKT) transition with two limiting conditions. We derive the renormalization group (RG) equations explicitly and also present the flow lines behavior. We also present the behavior of RG flow lines based on the exact solution. We observe that the physics of Majorana fermion zero modes and the gaped Ising-ferromagnetic phase, which appears in a different context. We observe that the evidence of gapless helical Luttinger liquid phase as a common non-topological quantum phase for both quantum BKT transitions. We explain analytically and physically that there is no Majorana-Ising transition. In the presence of chemical potential, the system shows the commensurate to incommensurate transition.

cond-mat.stat-mech↗

arXiv2020

An Interplay of Topology and Quantized Geometric Phase for two Different Symmetry-Class Hamiltonians

Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric phase along with the physical explanation for two different symmetry classes. We present a detailed study of the auxiliary space for two different symmetry classes of Hamiltonians. We show explicitly that the origin of the auxiliary space inside the curve is only a necessary condition but it is not a sufficient condition for the topological state. One of the most interesting results is that same symmetry-class Hamiltonians show different behaviour in topology and quantized geometric phase.

cond-mat.str-el↗

arXiv2020

A Study of Asymptotic Freedom like Behavior for Topological States of Matter

We present results for asymptotic freedom like behavior for the topological state of the helical spin liquid system with finite proximity induced superconducting gap. We derive two different quantum Berezinskii-Kosterlitz-Thouless (BKT) equations for the two different limit of this model Hamiltonian. The common quantum phase for these two quantum BKT transitions is the helical Luttinger liquid phase where there is no evidence of asymptotic freedom. There is no evidence of superconductor-insulator transition for this asymptotic freedom study. We observe the evidance of asymptotic freedom for the two model Hamiltonian, but the character of the asymptotic phases are different. We also observe that the Luttinger liquid parameter plays a significant role to determine the asymptotic freedom but the chemical potential has no effect on it.

cond-mat.mes-hall↗

arXiv2019

Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes

Symmetry plays an important role in the topological states of quantum matter. Cartan found three symmetry classes, Altland and Zirnbauer extended it to the ten-fold symmetry class for mesoscopic systems. We observe emergence of a new symmetry class for BdG Hamiltonians. This new symmetry class appears for the BdG Hamiltonian in spinful background. We also observe the interesting feature that there is no evidence of Kramers's degeneracy for this BdG model Hamiltonian either in spinless or in spinful background. We call the extra symmetry class X, i.e, expanding the ten-fold symmetry classes for topological states of quantum matter. These BdG show many new, interesting and insightful results.

cond-mat.str-el↗