arXiv subjects

Diptiman Sen

Publications and source records attributed to Diptiman Sen.

At least 37 records · Page 2Linked to original sources

arXiv2024

Phases and phase transitions in a dimerized spin-$\mathbf{\frac{1}{2}}$ XXZ chain

We revisit the phase diagram of the dimerized XXZ spin-$\frac{1}{2}$ chain with nearest-neighbor couplings which was studied numerically in Phys. Rev. B 106, L201106 (2022). The model has isotropic $XY$ couplings which have a uniform value and $ZZ$ couplings which have a dimerized form, with strengths $J_a$ and $J_b$ on alternate bonds. We find a rich phase diagram in the region of positive $J_a, ~J_b$. We provide a detailed understanding of the different phases and associated quantum phase transitions using a combination of mean-field theory, low-energy effective Hamiltonians, renormalization group calculations employing the technique of bosonization, and numerical calculations using the density-matrix renormalization group (DMRG) method. The phase diagram consists of two Ising paramagnetic phases called IPM$_0$ and IPM$_π$, and a phase with Ising Neel order called IN; all these phases are gapped. The phases IPM$_0$ and IPM$_π$ are separated by a gapless phase transition line given by $0 \le J_a = J_b \le 1$ which is described by a conformal field theory with central charge $c=1$. There are two gapless phase transition lines separating IPM$_0$ from IN and IPM$_π$ from IN; these are described by conformal field theories with $c=\frac{1}{2}$ corresponding to quantum Ising transitions. The $c=1$ line bifurcates into the two $c=\frac{1}{2}$ lines at the point $J_a = J_b = 1$; the shape of the bifurcation is found analytically using RG calculations. A symmetry analysis shows that IPM$_0$ is a topologically trivial phase while IPM$_π$ is a time-reversal symmetry-protected topological phase (SPT) with spin-$\frac{1}{2}$ states at the two ends of an open system. The numerical results obtained by the DMRG method are in good agreement with the analytical results. Finally we propose experimental platforms for testing our results.

cond-mat.str-el↗

arXiv2024

Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain

We study the disconnected entanglement entropy (DEE) of a Kitaev chain in which the chemical potential is periodically modulated with $δ$-function pulses within the framework of Floquet theory. For this driving protocol, the DEE of a sufficiently large system with open boundary conditions turns out to be integer-quantized, with the integer being equal to the number of Majorana edge modes localized at each edge of the chain generated by the periodic driving, thereby establishing the DEE as a marker for detecting Floquet Majorana edge modes. Analysing the DEE, we further show that these Majorana edge modes are robust against weak spatial disorder and temporal noise. Interestingly, we find that the DEE may, in some cases, also detect the anomalous edge modes which can be generated by periodic driving of the nearest-neighbor hopping, even though such modes have no topological significance and not robust against spatial disorder. We also probe the behaviour of the DEE for a kicked Ising chain in the presence of an integrability breaking interaction which has been experimentally realized.

cond-mat.stat-mech↗

arXiv2024

Subspace restricted thermalization in a correlated-hopping model with strong Hilbert space fragmentation characterized by irreducible strings

We introduce a one-dimensional correlated-hopping model of spinless fermions in which a particle can hop between two neighboring sites only if the sites to the left and right of those two sites have different particle numbers. Using a bond-to-site mapping, this model involving four-site terms can be mapped to an assisted pair-flipping model involving only three-site terms. This model shows strong Hilbert space fragmentation (HSF). We define irreducible strings (IS) to label the different fragments, determine the number of fragments, and the sizes of fragments corresponding to some special IS. In some classes of fragments, the Hamiltonian can be diagonalized completely, and in others it can be seen to have a structure characteristic of models which are not fully integrable. In the largest fragment in our model, the number of states grows exponentially with the system size, but the ratio of this number to the total Hilbert space size tends to zero exponentially in the thermodynamic limit. Within this fragment, we provide numerical evidence that only a weak version of the eigenstate thermalization hypothesis (ETH) remains valid; we call this subspace-restricted ETH. To understand the out-of-equilibrium dynamics of the model, we study the infinite-temperature time-dependent autocorrelation functions starting from a random initial state; we find that these exhibit a different behavior near the boundary compared to the bulk. Finally we propose an experimental setup to realize our correlated-hopping model.

cond-mat.stat-mech↗

arXiv2024

Electric field tunable edge transport in Bernal stacked trilayer graphene

This letter presents a non-local study on the electric field tunable edge transport in an hBN-encapsulated dual-gated Bernal stacked (ABA) trilayer graphene across various displacement fields ($D$) and temperatures ($T$). Our measurements revealed that the non-local resistance ($R_{NL}$) surpassed the expected classical ohmic contribution by a factor of at least two orders of magnitude. Through scaling analysis, we found that the non-local resistance scales linearly with the local resistance ($R_{L}$) only when the $D$ exceeds a critical value of $\sim0.2$ V/nm. Additionally, we observed that the scaling exponent remains constant at unity for temperatures below the bulk-band gap energy threshold ($T<25$ K). Further, the value of $R_{NL}$ decreases in a linear fashion as the channel length ($L$) increases. These experimental findings provide evidence for edge-mediated charge transport in ABA trilayer graphene under the influence of a finite displacement field. Furthermore, our theoretical calculations support these results by demonstrating the emergence of dispersive edge modes within the bulk-band gap energy range when a sufficient displacement field is applied.

cond-mat.mes-hall↗

arXiv2024

Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems

We study if the interplay between dynamical localization and interactions in periodically driven quantum systems can give rise to anomalous thermalization behavior. Specifically, we consider one-dimensional models with interacting spinless fermions with nearest-neighbor hopping and density-density interactions, and a periodically driven on-site potential with spatial periodicity $m=2$ and $m=4$. At a dynamical localization point, these models evade thermalization either due to the presence of an extensive number of conserved quantities (for weak interactions) or due to the kinetic constraints caused by drive-induced resonances (for strong interactions). Our models therefore illustrate interesting mechanisms for generating constrained dynamics in Floquet systems which are difficult to realize in an undriven system.

cond-mat.stat-mech↗

arXiv2024

Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical point with a continuous phase transition. We compute the critical exponents $z$, $β$, $γ$ and $ν$, and the central charge $c$ numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both $z$ and $c$ are equal to $1$, implying that the critical point is governed by a conformal field theory. The values obtained for $β/ν$, $γ/ν$, and $ν$ from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. An analysis on larger systems but with open boundaries using density-matrix renormalization group calculations, however, shows that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates. A subset of these eigenstates have wave functions which are independent of $h$ and have unusual entanglement structure, suggesting that they are quantum many-body scars. The number of such states scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if $h \gg 1$ or $h \ll 1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

cond-mat.stat-mech↗

arXiv2023

Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain

The action of any local operator on a quantum system propagates through the system carrying the information of the operator. This is usually studied via the out-of-time-order correlator (OTOC). We numerically study the information propagation from one end of a periodically driven spin-1/2 $XY$ chain with open boundary conditions using the Floquet infinite-temperature OTOC. We calculate the OTOC for two different spin operators, $σ^x$ and $σ^z$. For sinusoidal driving, the model can be shown to host different types of edge states, namely, topological (Majorana) edge states and non-topological edge states. We observe a localization of information at the edge for both $σ^z$ and $σ^x$ OTOCs whenever edge states are present. In addition, in the case of non-topological edge states, we see oscillations of the OTOC in time near the edge, the oscillation period being inversely proportional to the gap between the Floquet eigenvalues of the edge states. We provide an analytical understanding of these effects due to the edge states. It was known earlier that the OTOC for the spin operator which is local in terms of Jordan-Wigner fermions ($σ^z$) shows no signature of information scrambling inside the light cone of propagation, while the OTOC for the spin operator which is non-local in terms of Jordan-Wigner fermions ($σ^x$) shows signatures of scrambling. We report a remarkable `unscrambling effect' in the $σ^x$ OTOC after reflections from the ends of the system. Finally, we demonstrate that the information propagates into the system mainly via the bulk states with the maximum value of the group velocity, and we show how this velocity is controlled by the driving frequency and amplitude.

cond-mat.stat-mech↗

arXiv2023

Mechanisms of scrambling and unscrambling of quantum information in the ground state in spin chains: domain-walls, spin-flips and scattering phase shifts

The spatiotemporal evolution of the out-of-time-order correlator (OTOC) measures the propagation and scrambling of local quantum information. For the transverse field Ising model with open boundaries, the local operator $σ^{x}$ shows an interesting picture of the ground state OTOC where the local information gets scrambled throughout the entire system and, more strikingly, starts `unscrambling' upon reflection at the other end. Earlier discussions of OTOCs did not explain the physical processes responsible for such scrambling and unscrambling of information. We explicitly show that in the paramagnetic phase, the scrambling and unscrambling is due to the scattering of a pair of low-energy spin-flip excitations, even in the presence of small interactions. In the ferromagnetic phase the same phenomena are explained by the motion of a domain-wall excitation. Thus, in different limits of the system parameters, we have provided a simple and almost complete understanding of the space-time pictures of the OTOCs, including the unscrambling, in terms of the low-energy excitations like one and two spin-flips or a single domain wall.

cond-mat.str-el↗

arXiv2023

Detecting prethermal Floquet phases of Rydberg atom arrays

We study the prethermal Floquet phases of a two-dimensional (2D) Rydberg atom array on a rectangular lattice in the presence of a periodic drive with large drive amplitude. We derive an analytic, albeit perturbative, Floquet Hamiltonian using Floquet perturbation theory (FPT) which charts out these phases and shows that the transition between them can be accessed by tuning the drive frequency. Using both numerical exact diagonalization on finite-size arrays and analytical first-order Floquet Hamiltonian derived using FPT, we show that these prethermal Floquet phases and the transitions between them can be detected by studying the dynamics of equal-time density-density correlation functions of the Rydberg atoms. Our analysis thus provides a simple way of detecting these phases and associated transitions in this system; such a detection can be achieved in standard experiments which we discuss.

cond-mat.str-el↗

arXiv2023

Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states

We study if periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases which have no counterparts in the static model. Specifically, we consider the Aubry-André model which is a one-dimensional time-independent model with an on-site quasiperiodic potential $V_0$ and a nearest-neighbor hopping amplitude which is taken to have a staggered form. We add a uniform hopping amplitude which varies periodically in time with a frequency $ω$. Unlike the static Aubry-André model which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases: a phase with only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios which scale with the system size with exponents which are different from the values for both extended and localized states. In addition, we observe intricate re-entrant transitions between the different kinds of states when $ω$ and $V_0$ are varied. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet and find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a non-monotonic dependence on $V_0$ which does not occur in the static model. We conclude that the interplay of quasiperiodic potential and driving produces a rich phase diagram which does not appear in the static model.

cond-mat.dis-nn↗

arXiv2022

Experimental observation of spin-split energy dispersion in high-mobility single-layer graphene/WSe2 heterostructures

Proximity-induced spin-orbit coupling in graphene has led to the observation of intriguing phenomena like time-reversal invariant $\mathbb{Z}_2$ topological phase and spin-orbital filtering effects. An understanding of the effect of spin-orbit coupling on the band structure of graphene is essential if these exciting observations are to be transformed into real-world applications. In this research article, we report the experimental determination of the band structure of single-layer graphene (SLG) in the presence of strong proximity-induced spin-orbit coupling. We achieve this in high-mobility hBN-encapsulated SLG/WSe2 heterostructures through measurements of quantum oscillations. We observe clear spin-splitting of the graphene bands along with a substantial increase in the Fermi velocity. Using a theoretical model with realistic parameters to fit our experimental data, we uncover evidence of a band gap opening and band inversion in the SLG. Further, we establish that the deviation of the low-energy band structure from pristine SLG is determined primarily by the valley-Zeeman SOC and Rashba SOC, with the Kane-Mele SOC being inconsequential. Despite robust theoretical predictions and observations of band-splitting, a quantitative measure of the spin-splitting of the valence and the conduction bands and the consequent low-energy dispersion relation in SLG was missing -- our combined experimental and theoretical study fills this lacuna.

cond-mat.mes-hall↗

arXiv2022

Engineering Floquet topological phases using elliptically polarized light

We study a two-dimensional topological system driven out of equilibrium by the application of elliptically polarized light. In particular, we analyze the Bernevig-Hughes-Zhang model when it is perturbed using an elliptically polarized light of frequency $Ω$ described in general by a vector potential ${\bf A}(t) = (A_{0x} \cos(Ωt), A_{0y} \cos(Ωt + ϕ_0))$. (Linear and circular polarizations can be obtained as special cases of this general form by appropriately choosing $A_{0x}$, $A_{0y}$, and $ϕ_0$). Even for a fixed value of $ϕ_0$, we can change the topological character of the system by changing the ratio of the $x$ and $y$ components of the drive. We therefore find a rich topological phase diagram as a function of $A_{0x}$, $A_{0y}$ and $ϕ_0$. In each of these phases, the topological invariant given by the Chern number is consistent with the number of spin-polarized states present at the edges of a nanoribbon.

cond-mat.mes-hall↗

arXiv2022

Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term

We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When the on-site interaction $U$ is much larger than the hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_α,J_β,J_γ)$ on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry (TRS), $H_{eff}$ is also found to have a chiral three-spin interaction in each triangle, with the coefficient $C$ of the interaction having opposite signs on up- and down-pointing triangles. Thus periodic driving which breaks TRS can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters $(J_α,J_β,J_γ,C)$ depend on the amplitude, frequency and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (colinear and coplanar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.

cond-mat.str-el↗

arXiv2021

Dynamical relaxation of correlators in periodically driven integrable quantum systems

We show that the correlation functions of a class of periodically driven integrable closed quantum systems approach their steady state value as $n^{-(α+1)/β}$, where $n$ is the number of drive cycles and $α$ and $β$ denote positive integers. We find that generically $β=2$ within a dynamical phase characterized by a fixed $α$; however, its value can change to $β=3$ or $β=4$ either at critical drive frequencies separating two dynamical phases or at special points within a phase. We show that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and one-dimensional (1D) transverse field Ising models, discuss the role of symmetries of the Floquet spectrum in determining $β$, and chart out the values of $α$ and $β$ realized in these models. We analyze the SSH model for a continuous drive protocol using a Floquet perturbation theory which provides analytical insight into the behavior of the correlation functions in terms of its Floquet Hamiltonian. This is supplemented by an exact numerical study of a similar behavior for the 1D Ising model driven by a square pulse protocol. For both models, we find a crossover timescale $n_c$ which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency, $ω_c$, is approached from below ($ω< ω_c$). We tie such behavior to the presence of multiple stationary points in the Floquet spectrum of these models and provide an analytic expression for the time period of these oscillations.

cond-mat.stat-mech↗

arXiv2021

Driven quantum many-body systems and out-of-equilibrium topology

In this review we present some of the work done in India in the area of driven and out-of-equilibrium systems with topological phases. After presenting some well-known examples of topological systems in one and two dimensions, we discuss the effects of periodic driving in some of them. We discuss the unitary as well as the non-unitary dynamical preparation of topologically non-trivial states in one and two dimensional systems. We then discuss the effects of Majorana end modes on transport through a Kitaev chain and a junction of three Kitaev chains. Transport through the surface states of a three-dimensional topological insulator is discussed. The effects of hybridization between the top and bottom surfaces and the application of electromagnetic radiation on a strip-like region on the top surface are described. Two unusual topological systems are mentioned briefly, namely, a spin system on a kagome lattice and a Josephson junction of three superconducting wires. We have also included a pedagogical discussion on topology and topological invariants in the appendices, where the connection between topological properties and the intrinsic geometry of quantum states is also elucidated.

cond-mat.stat-mech↗

arXiv2021

Bosonization study of a generalized statistics model with four Fermi points

We study a one-dimensional lattice model of fractional statistics in which particles have next-nearest-neighbor hopping between sites which depends on the occupation number at the intermediate site and a statistical parameter $ϕ$. The model breaks parity and time-reversal symmetries and has four-fermion interactions if $ϕ\ne 0$. We first analyze the model using mean field theory and find that there are four Fermi points whose locations depend on $ϕ$ and the filling $η$. We then study the modes near the Fermi points using the technique of bosonization. Based on the quadratic terms in the bosonized Hamiltonian, we find that the low-energy modes form two decoupled Tomonaga-Luttinger liquids with different values of the Luttinger parameters which depend on $ϕ$ and $η$; further, the right and left moving modes of each system have different velocities. A study of the scaling dimensions of the cosine terms in the Hamiltonian indicates that the terms appearing in one of the Tomonaga-Luttinger liquids will flow under the renormalization group and the system may reach a non-trivial fixed point in the long distance limit. We examine the scaling dimensions of various charge density and superconducting order parameters to find which of them is the most relevant for different values of $ϕ$ and $η$. Finally we look at two-particle bound states that appear in this system and discuss their possible relevance to the properties of the system in the thermodynamic limit. Our work shows that the low-energy properties of this model of fractional statistics have a rich structure as a function of $ϕ$ and $η$.

cond-mat.str-el↗

arXiv2021

Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases

We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that an appropriately defined Chern number accurately maps out all the possible phases of the system and remains well-defined even in the presence of degeneracies in the occupied bands. Importantly, our result paves the way for realizing adiabatic preparation of monolayer Chern insulators. This has been a major challenge till date, given the impossibility of unitarily connecting inequivalent topological phases. We show that this difficulty can be circumvented by adiabatically varying the interlayer coupling in such a way that the system remains gapped at all times. In particular, a complete knowledge of the phase diagram of the bilayer composite immediately allows one to identify all such adiabatic passages which may connect the different Chern inequivalent phases of the individual monolayers.

cond-mat.stat-mech↗

arXiv2021

Dynamical Freezing and Scar Points in Strongly Driven Floquet Matter: Resonance vs Emergent Conservation Laws

We consider a clean quantum system subject to strong periodic driving. The existence of a dominant energy scale, $h_D^x$, can generate considerable structure in an effective description of a system which, in the absence of the drive, is non-integrable, interacting, and does not host localization. In particular, we uncover points of freezing in the space of drive parameters (frequency and amplitude). At those points, the dynamics is severely constrained due to the emergence of an almost exact local conserved quantity, which scars the {\it entire} Floquet spectrum by preventing the system from heating up ergodically, starting from any generic state, even though it delocalizes over an appropriate subspace. At large drive frequencies, where a naïve Magnus expansion would predict a vanishing effective (average) drive, we devise instead a strong-drive Magnus expansion in a moving frame. There, the emergent conservation law is reflected in the appearance of an `integrability' of an effective Hamiltonian. These results hold for a wide variety of Hamiltonians, including the Ising model in a transverse field in {\it any dimension} and for {\it any form of Ising interactions}. The phenomenon is also shown to be robust in the presence of {\it two-body Heisenberg interactions with any arbitrary choice of couplings}. Further, we construct a real-time perturbation theory which captures resonance phenomena where the conservation breaks down, giving way to unbounded heating. This opens a window on the low-frequency regime where the Magnus expansion fails.

cond-mat.other↗