arXiv subjects

Adhip Agarwala

Publications and source records attributed to Adhip Agarwala.

At least 37 records · Page 2Linked to original sources

arXiv2024

Spectral Form Factors of Topological Phases

Signatures of dynamical quantum phase transitions and chaos can be found in the time evolution of generalized partition functions such as spectral form factors (SFF) and Loschmidt echoes. While a lot of work has focused on the nature of such systems in a variety of strongly interacting quantum theories, in this work, we study their behavior in short-range entangled topological phases, particularly focusing on the role of symmetry-protected topological zero modes. We show, using both analytical and numerical methods, how the existence of such zero modes in any representative system can mask the SFF with large period (akin to generalized Rabi) oscillations, hiding any behavior arising from the bulk of the spectrum. Moreover, in a quenched disordered system, these zero modes fundamentally change the late-time universal behavior reflecting the chaotic signatures of the zero-energy manifold. Our study uncovers the rich physics underlying the interplay of chaotic signatures and topological characteristics in a quantum system.

cond-mat.str-el↗

arXiv2024

Dimensional reduction of Kitaev spin liquid at quantum criticality

We investigate the fate of the Kitaev spin liquid (KSL) under the influence of an external magnetic field $h$ in the [001] direction and upon tuning bond anisotropy of the Kitaev coupling $K_z$ keeping $K_x = K_y = K$. Guided by density matrix renormalization group, exact diagonalization, and with insights from parton mean field theory, we uncover a field-induced gapless-to-gapless Lifshitz transition from the nodal KSL to an intermediate gapless phase. The intermediate phase sandwiched between $h_{c1}$ and $h_{c2}$, which persists for a wide range of anisotropy $K_z/K > 0$, is composed of weakly coupled one-dimensional quantum critical chains. This intermediate phase is a dimensional crossover which asymptotically leads to the one-dimensional quantum Ising criticality characterized by the (1+1)D conformal field theory as the field reaches the phase transition at $h_{c2}$. Beyond $h_{c2}$ the system enters a partially polarized phase describable as effectively decoupled bosonic chains in which spin waves propagate along the one-dimensional zigzag direction. Our findings provide a comprehensive phase diagram and offer insights into the unusual physics of dimensional reduction generated by a uniform magnetic field in an otherwise two-dimensional quantum spin liquid.

cond-mat.str-el↗

arXiv2023

Percolation Transition in a Topological Phase

Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an underlying topological phase. To understand this physics we introduce and study both short and long-ranged toy models where a one dimensional topological phase is subjected to bond percolation protocols. We find that non-trivial boundary phenomena follow competing energy scales even while global topological response is governed via geometrical properties of the percolated lattice. Using numerical, analytical and appropriate mean-field studies we uncover the rich phenomenology and the various cross-over regimes of these systems. In particular, we discuss emergence of "fractured topological region" where an overall trivial system contains macroscopic number of topological clusters. Our study shows the interesting physics that can arise from an interplay of geometrical disorder within a topological phase.

cond-mat.dis-nn↗

arXiv2023

Anyon dynamics in field-driven phases of the anisotropic Kitaev model

The Kitaev model on a honeycomb lattice with bond-dependent Ising interactions offers an exactly solvable model of a quantum spin liquid (QSL) with gapped $Z_2$ fluxes and gapless linearly dispersing Majorana fermions in the isotropic limit ($K_x=K_y=K_z$). We explore the phase diagram along two axes, an external magnetic field, $h$, applied out-of-plane of the honeycomb, and anisotropic interactions, $K_z$ larger than the other two. For $K_z/K\gg 2$ and $h=0$, the matter Majorana fermions have the largest gap, and the system is described by a gapped $Z_2$ Toric code in which the $Z_2$ fluxes form the low energy bosonic Ising electric (e) and magnetic (m) charges along with their fermionic bound state $ε=e\times m$. In this regime, we find that a small out-of-plane magnetic field creates $ε$ fermions that disperse in fixed one-dimensional directions before the transition to a valence bond solid phase, providing a direct dynamical signature of low energy $Z_2$ Abelian flux excitations separated from the Majorana sector. At lower $K_z$ in the center of the Abelian phase, in a regime we dub the primordial fractionalized (PF) regime, the field generates a hybridization between the $ε$ fermions and the Majorana matter fermions, resulting in a $ψ$ fermion. All the other phases in the field-anisotropy plane are naturally obtained from this primordial soup. We show that in the $Z_2$ Abelian phase, including the PF regime, the dynamical structure factors of local spin flip operators reveal distinct peaks that can be identified as arising from different anyonic excitations. We present in detail their signatures in energy and momentum and propose their identification by inelastic light scattering or inelastic polarized neutron scattering as ``smoking gun" signatures of fractionalization in the QSL phase.

cond-mat.str-el↗

arXiv2023

Correlation-driven non-trivial phases in single bi-layer Kagome intermetallics

Bi-layer Kagome compounds provide an exciting playground where the interplay of topology and strong correlations can give rise to exotic phases of matter. Motivated by recent first principles calculation on such systems (Phys. Rev. Lett 125, 026401), reporting stabilization of a Chern metal with topological nearly-flat band close to Fermi level, we build minimal models to study the effect of strong electron-electron interactions on such a Chern metal. Using approriate numerical and analytical techniques, we show that the topologically non-trivial bands present in this system at the Fermi energy can realize fractional Chern insulator states. We further show that if the time-reversal symmetry is restored due to destruction of magnetism by low dimensionality and fluctuation, the system can realize a superconducting phase in the presence of strong local repulsive interactions. Furthermore, we identify an interesting phase transition from the superconducting phase to a correlated metal by tuning nearest-neighbor repulsion. Our study uncovers a rich set of non-trivial phases realizable in this system, and contextualizes the physically meaningful regimes where such phases can be further explored.

cond-mat.str-el↗

arXiv2023

Classical and quantum facilitated exclusion processes

We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical facilitated process engineers an interesting $quantum$ $absorbing$ $transition$ where the quantum particles transit from an unentangled direct-product absorbing phase to an entangled steady state with a finite current at density $ρ=1/2$. In the generalised classical facilitated exclusion process, which includes independent hopping of particles with rate $p$, our analytical and Monte-Carlo results establish emergence of a special density $ρ^*=1/3$ that demarcates two regimes in the steady state, based on the competition between two current carrying modes (facilitated and independent). The corresponding quantum system also displays similar qualitative behaviours with striking non-monotonic features in the bipartite entanglement. Our work ties the two sub-fields of classically interacting exclusion processes, and interacting non-Hermitian quantum Hamiltonians to show common themes in the non-equilibrium phases they realise.

cond-mat.stat-mech↗

arXiv2023

Fractionalization and topology in amorphous electronic solids

Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an amorphous setting. In this work, we extend these studies to incorporate the effect of strong repulsive interactions on the fate of topology and other correlation induced phenomena. Using a parton-based approach, we obtain the interacting phase diagram for an electronic two-orbital model with tunable topology in a two dimensional amorphous network. In addition to the (non-)topological phases that are adiabatically connected to the free fermion limit, we find a number of strongly interacting amorphous analogs of crystalline Mott insulating phases with non-trivial chiral neutral edge modes, and a fractionalized Anderson insulating phase. The amorphous networks thus provide a new playground for studying a plethora of exotic states of matter, and their glassy dynamics, due to the combined effects of non-trivial topology, disorder, and strong interactions.

cond-mat.str-el↗

arXiv2022

Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system

In this work we study many-body 'steady states' that arise in the non-Hermitian generalisation of the non-interacting Su-Schrieffer-Heeger model at a finite density of fermions. We find that the hitherto known phase diagrams for this system, derived from the single-particle gap closings, in fact correspond to distinct non-equilibrium phases, which either carry finite currents or are dynamical insulators where particles are entrapped. Each of these have distinct quasi-particle excitations and steady state correlations and entanglement properties. Looking at finite-sized systems, we further modulate the boundary to uncover the topological features in such steady states -- in particular the emergence of leaky boundary modes. Using a variety of analytical and numerical methods we develop a theoretical understanding of the various phases and their transitions, and uncover the rich interplay of non-equilibrium many-body physics, quantum entanglement and topology in a simple looking, yet a rich model system.

cond-mat.mes-hall↗

arXiv2021

Interaction driven giant thermopower in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MtBLG) has proven to be an extremely promising new platform to realize and study a host of emergent quantum phases arising from the strong correlations in its narrow bandwidth flat band. In this regard, thermal transport phenomena like thermopower, in addition to being coveted technologically, is also sensitive to the particle-hole (PH) asymmetry, making it a crucial tool to probe the underlying electronic structure of this material. We have carried out thermopower measurements of MtBLG as a function of carrier density, temperature and magnetic field, and report the observation of an unusually large thermopower reaching up to a value as high as $\sim \bf{100μV/K}$ at a low temperature of 1K. Surprisingly, our observed thermopower exhibiting peak-like features in close correspondence to the resistance peaks around the integer Moire fillings, including the Dirac Point, violating the Mott formula. %Surprisingly, our observed thermopower exhibits peak-like features in close correspondence to the resistance peaks around the integer Moire fillings, including the Dirac Point, which completely violates the Mott formula. We show that the large thermopower peaks and their %non-monotonic dependence with temperature and magnetic field associated behaviour arise from the emergent highly PH asymmetric electronic structure due to the cascade of Dirac revivals. Furthermore, the thermopower shows an anomalous peak around the superconducting transition on the hole side and points towards the possible role of enhanced superconducting fluctuations in MtBLG.

cond-mat.mes-hall↗

arXiv2021

Exploring ideas in topological quantum phenomena: A journey through the SSH model

Geared as an invitation for undergraduates, beginning graduate students, we present a pedagogical introduction to one-dimensional topological phases -- in particular the Su-Schrieffer-Heeger model. In the process, we delve upon ideas of entanglement using the correlator method and the von-Neumann density-matrix method, geometric phase, polarization, transport signatures and the role of electron-electron interactions. Through hands-on numerical experiments, whose $\href{https://github.com/hnoend/SSH_codes}{codes}$ are shared, we try to drive home the message why a program of simulating quantum electronics with topological toy models is the store house for discovering fantastic physics ideas.

cond-mat.mes-hall↗

arXiv2021

Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$Γ$ magnet

We study the Kitaev-Heisenberg-$Γ$ model with antiferromagnetic Kitaev exchanges in the strong anisotropic (toric code) limit to understand the phases and the intervening phase transitions between the gapped $Z_2$ quantum spin liquid and the spin-ordered (in the Heisenberg limit) as well as paramagnetic phases (in the pseudo-dipolar, $Γ$, limit). We find that the paramagnetic phase obtained in the large $Γ$ limit has no topological entanglement entropy and is proximate to a gapless critical point of a system described by an equal superposition of differently oriented stacked one-dimensional $Z_2\times Z_2$ symmetry protected topological phases. Using a combination of exact diagonalization calculations and field-theoretic analysis we map out the phases and phase transitions to reveal the complete phase diagram as a function of the Heisenberg, the Kitaev, and the pseudo-dipolar interactions. Our work shows a rich plethora of unconventional phases and phase transitions and provides a comprehensive understanding of the physics of anisotropic Kitaev-Heisenberg-$Γ$ systems along with our recent paper [Phys. Rev. B 102, 235124 (2020)] where the ferromagnetic Kitaev exchange was studied.

cond-mat.str-el↗

arXiv2020

Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains

We show that mutual statistics between quantum particles can be tuned to generate emergent novel few particle quantum mechanics for the boundary modes of symmetry-protected topological phases of matter. As a concrete setting, we study a system of pseudofermions, defined as quantum particles with tunable algebra, which lie on two distinct Su-Schrieffer-Heeger (SSH) chains. We find that as the mutual statistics of the particles are tuned -- the boundary modes present in the two chains gets non-trivially entangled showing a sudden jump in their mutual entanglement entropy. We further show that, such tuning of statistics engenders a first-order transition between two topologically non-trivial phases which differ in the behavior of inter-chain entanglement. Using a combination of analytical and numerical techniques and effective modeling, we uncover the rich physics that this system hosts. The results are of particular relevance in context of the study of the effective low energy quantum mechanics of topological edge modes in one hand and their recent realization in ultracold atoms on the other. This then provides for controlled manipulation of such low energy modes.

cond-mat.str-el↗

arXiv2020

Gapless state of interacting Majorana fermions in a strain-induced Landau level

Mechanical strain can generate a pseudo-magnetic field, and hence Landau levels (LL), for low energy excitations of quantum matter in two dimensions. We study the collective state of the fractionalised Majorana fermions arising from residual generic spin interactions in the central LL, where the projected Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and particle-hole symmetries forbid any bilinear couplings, leading to an intrinsically strongly interacting system; also, they allow the definition of a filling fraction, which is fixed at 1/2. We argue that the resulting many-body state is gapless within our numerical accuracy, implying ultra-short-ranged spin correlations, while chirality correlators decay algebraically. This amounts to a Kitaev `non-Fermi' spin liquid, and shows that interacting Majorana Fermions can exhibit intricate behaviour akin to fractional quantum Hall physics in an insulating magnet.

cond-mat.str-el↗

arXiv2020

Higher-order topological insulators in amorphous solids

We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two and three dimensional crystalline HOT insulators, accommodating topological corner states, we gradually enhance structural randomness in the system. Within a parameter regime, as long as amorphousness is confined by outer crystalline boundary, the system continues to host corner states, yielding amorphous HOT insulators. However, as structural disorder percolates to the edges, corner states start to dissolve into amorphous bulk, and ultimately the system becomes a trivial insulator when amorphousness plagues the entire system. These outcomes are further substantiated by computing the quadrupolar (octupolar) moment in two (three) dimensions. Therefore, HOT phases can be realized in amorphous solids, when wrapped by a thin (lithographically grown, for example) crystalline layer. Our findings suggest that crystalline topological phases can be realized even in the absence of local crystalline symmetry.

cond-mat.mes-hall↗

arXiv2019

Topological and conventional phases of a three dimensional electron glass

We investigate a symmetry protected $Z_2$ topological electron glass -- a glassy equivalent of the $Z_2$ topological band insulator in crystalline systems -- and uncover associated quantum phase transitions in this three dimensional amorphous network of atoms. Through explicit numerical calculations of the Witten effect, we show that the $Z_2$ glass is characterized by an anomalous electromagnetic response -- dyons with 1/2 electronic charge. We further study, using a variety of numerical diagnostics including such electromagnetic responses, the phase transitions of the $Z_2$ glass into a metallic and/or a trivial insulating phase. We find that the phase transitions here are governed by subtle features of mobility edges and "spectral inversion" which are possibly unique to structurally amorphous systems. Our results provide a concrete setting to understand the general underpinnings of such phases -- where strong structural disorder interplays with symmetry-protected topological order.

cond-mat.dis-nn↗

arXiv2018

Statistics-tuned phases of pseudofermions in one dimension

We show that a quadratic system of pseudofermions, with tunable fractionalised statistics, can host a rich phase diagram on a one dimensional chain with nearest and next nearest neighbor hopping. Using a combination of numerical and analytical techniques, we show that that by varying the statistical angle and the ratio of the hopping, the system stabilizes two Tomonaga-Luttinger liquids (TLL) with central charges c = 1 and 2 respectively along with the inversion symmetry broken bond ordered (BO) insulating phase. Interestingly, the two quantum phase transitions in the system - (1) between the two TLLs, and, (2) the c = 1 TLL and BO phase can be engendered by solely tuning the statistics of the pseudofermions. Our analysis shows that both these transition are continuous and novel with the former lacking a local order-parameter based description and the latter of Berezinskii-Kosterlitz-Thouless type. These phases and phase transitions can be of direct experimental relevance in context of recent studies of fermionic cold atoms.

cond-mat.str-el↗

arXiv2018

Fractalized Metals

The classification of gapped phases of non-interacting fermions hinges on the tenfold symmetries and on the spatial dimension. The notion of dimension leads to a well defined demarcation between bulk and edge. Here we explore the nature of topological phases in systems where the distinction between bulk and edge is nebulous, of which fractal lattices are canonical examples. Our key finding is that in homogeneous fractal lattices (where every site is equally coordinated), there are no gapped topological phases. What appears instead is a novel metallic state -- the fractalized metal -- whose low energy states arrange hierarchically on the structure of the fractal that hosts them. We study the properties (such as chiral transport) of this metal and demonstrate its robustness to disorder. Further, by studying a variety of fractal models we establish that the homogeneity of the fractal is a key condition for the realization of such fractalized metallic states.

cond-mat.dis-nn↗

arXiv2017

Effects of local periodic driving on transport and generation of bound states

We periodically kick a local region in a one-dimensional lattice and demonstrate, by studying wave packet dynamics, that the strength and the time period of the kicking can be used as tuning parameters to control the transmission probability across the region. Interestingly, we can tune the transmission to zero which is otherwise impossible to do in a time-independent system. We adapt the non-equilibrium Green's function method to take into account the effects of periodic driving; the results obtained by this method agree with those found by wave packet dynamics if the time period is small. We discover that Floquet bound states can exist in certain ranges of parameters; when the driving frequency is decreased, these states get delocalized and turn into resonances by mixing with the Floquet bulk states. We extend these results to incorporate the effects of local interactions at the driven site, and we find some interesting features in the transmission and the bound states.

cond-mat.mes-hall↗