arXiv subjects

Aditi Mitra

Publications and source records attributed to Aditi Mitra.

At least 19 recordsLinked to original sources

arXiv2026

State preparation via measurement and feedback: pushing relations, state structures, and non-invertible symmetries

Quantum circuits with measurements and unitary feedback (MF) can prepare long-range entangled states in constant depth, but a systematic construction of the MF preparation circuit for a given target state remains underexplored. We develop such a scheme for one-dimensional states, based on the notion of pushable defects: virtual-bond operators of a matrix product state that can be pushed through the tensor at the price of a physical feedback unitary. We show that the set of pushable defects, together with their pushing relations classifies finite-depth MF-preparable states and dictates their preparation circuits. To each class of the target state $|A\rangle$, we associate a state $|B\rangle$ from which $|A\rangle$ can be prepared using a 1-round MF circuit; in particular, $|A\rangle$ is preparable from a product state using a circuit with 1 round of MF whenever $|B\rangle$ is preparable by a finite-depth local unitary (FDLU) circuit. For a general target state, the scheme is obtained by iterating this procedure until the associated state is FDLU-preparable. For open-boundary matrix product states, the scheme is complete: it constructs a preparation circuit whenever finite-depth MF preparation with left-conditioned feedback corrections is possible. Pushable defects and pushing relations thus emerge as a unifying principle for quantum state preparation via measurements and feedback. This characterization further reveals an intrinsic connection between MF circuits and non-invertible symmetries: states with certain classes of pushing relations are related to a product state by Tambara-Yamagami duality operators, or by continuous cosine symmetry operators with fusion rules $L_α L_{α'} = L_{α+α'} + L_{α-α'}$, together with their generalizations up to (not necessarily transversal) gates.

quant-ph↗

arXiv2026

Non-invertible symmetries out of equilibrium: Eigenstate order and Floquet physics

Through the study of the Rep($D_8$) non-invertible symmetry, we show how non-invertible symmetries manifest in dynamics. Results are presented for dynamics generated by Hamiltonians as well as Floquet unitaries. For both examples, the role of the non-invertible symmetry is studied through the appearance of non-invertible symmetry protected edge modes. In addition, the role of the non-invertible symmetry for the Hamiltonian is studied through eigenstate order. In particular, by considering the effect of symmetry preserving disorder, the non-invertible symmetry is shown to give rise to degeneracies in the spectra of the Hamiltonian that can only be completely lifted at orders of perturbation that scale with system size. The eigenstates of disordered Hamiltonians, whose ground states correspond to non-trivial symmetry protected topological (SPT) states, are shown to have either trivial or non-trivial SPT order that are detected as non-zero expectation value of string order-parameters. In contrast, non-trivial SPT order is absent in the eigenstates of trivial SPT Hamiltonians with disorder. The interface between two different SPT phases host edge modes whose dynamics is studied numerically and analytically. The edge mode is shown to oscillate at frequencies related to different effective chain lengths that are weighted by the temperature, becoming an exact zero mode in the limit of zero temperature. A Floquet model with the non-invertible symmetry is constructed whose edge mode is shown to exhibit period-doubled dynamics at low effective-temperatures. The zero and period-doubled edge modes differ from those in conventional SPTs by being symmetric under the invertible symmetry, while being charged under the non-invertible symmetry.

cond-mat.str-el↗

arXiv2026

Anderson Localization: A Floquet operator Krylov space perspective

The problem of Anderson localization, as well as the single particle localization-delocalizaton transition of the Aubry-André model, is studied employing operator Krylov space methods. It is shown that even when the dynamics is generated by a Hamiltonian, studying the dynamics at stroboscopic rather than continuous times has its advantages. In particular, mapping the dynamics to an effective Floquet problem results in an operator Krylov space description where quantities such as the spectral function can be computed with fewer computational resources, while a moment method exists that allows for the extraction of Krylov parameters directly from the discrete time autocorrelation function. For stroboscopic dynamics, the operator Krylov space corresponds to the dynamics of an edge operator of an inhomogeneous Floquet transverse field Ising model, with the parameters of this effective model generated recursively. The Krylov parameters show disorder-averaged renormalization with their distribution narrowing as the recursion step increases. It is shown that a more physical spectral function is obtained from the Krylov parameters obtained from the disorder-averaged autocorrelation function, rather than the disorder-averaged Krylov parameters. The delocalized (localized) phase is shown to correspond to the appearance (absence) of a Porter-Thomas distribution, a ballistically propagating (localized) wavefront in operator Krylov space, and a smooth (discrete) Berstein-Szegö power-spectrum. The localization-delocalization transition is also demonstrated in operator Krylov space. A Porter-Thomas distribution is also observed at the critical point. The long-time dynamics and the inverse participation ratio at the critical point is shown to exhibit behavior consistent with a multi-fractal scaling with system size.

cond-mat.dis-nn↗

arXiv2026

Topological Floquet Green's function zeros

Motivated by recent advances in digital quantum emulation using noisy intermediate-scale quantum (NISQ) devices and an increased interest in topological Green's function zeros in condensed matter systems, we here study Green's function zeros in topological Floquet systems. We concentrate on interacting Kitaev-like Floquet chains (or equivalently transverse field Ising circuits) and introduce Floquet Green's-function-based topological invariants for the corresponding symmetry class BDI. In the vicinity of special points in the free fermion phase diagram and using tailor-made interactions which lead to the Floquet version of symmetric mass generation, we analytically calculate both edge and bulk Green's functions. Just as in the case of continuum time evolution, topological bands of Green's function zeros may also contribute to the topological invariant. However, contrary to the case of continuum time evolution, Floquet Green's functions can have zeros even in the absence of interactions. Finally, we also discuss an implementation of this Floquet system in a digital quantum emulator: We present a circuit which encodes the interaction under consideration and pinpoint the observables carrying information about the topological Green's function boundary zeros.

cond-mat.mes-hall↗

arXiv2026

Floquet operator dynamics and orthogonal polynomials on the unit circle

Operator spreading under stroboscopic time evolution due to a unitary is studied. An operator Krylov space is constructed and related to orthogonal polynomials on a unit circle (OPUC), as well as to the Krylov space of the edge operator of the Floquet transverse field Ising model with inhomogeneous couplings (ITFIM). The Verblunsky coefficients in the OPUC representation are related to the Krylov angles parameterizing the ITFIM. The relations between the OPUC and spectral functions are summarized and several applications are presented. These include derivation of analytic expressions for the OPUC for persistent $m$-periodic dynamics, and the numerical construction of the OPUC for autocorrelations of the homogeneous Floquet-Ising model as well as the $Z_3$ clock model. The numerically obtained Krylov angles of the $Z_3$ clock model with long-lived period tripled autocorrelations show a spatial periodicity of six, and this observation is used to develop an analytically solvable model for the ITFIM that mimics this behavior.

cond-mat.str-el↗

arXiv2025

Isolated zero mode in a quantum computer from a duality twist

Investigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single zero mode. This zero mode is unusual as it lacks a localized partner in the same $\mathbb{Z}_2$ sector and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality transformation. Finally, we highlight the robustness of the isolated zero mode to integrability- and symmetry-breaking perturbations. Our findings provide a method for exploring exotic topological defects, associated with noninvertible generalized symmetries, in digitized quantum devices.

quant-ph↗

arXiv2025

Classification of Thouless pumps with non-invertible symmetries and implications for Floquet phases

We study symmetry preserving adiabatic and Floquet dynamics of one-dimensional systems. Using quasiadiabatic evolution, we establish a correspondence between adiabatic cycles and invertible defects generated by spatially truncated Thouless pump operators. Employing the classification of gapped phases by module categories, we show that the Thouless pumps are classified by the group of autoequivalences of the module category. We then explicitly construct Thouless pump operators for minimal lattice models with $\text{Vec}_G$, Rep($G$), and Rep($H$) symmetries, and show how the Thouless pump operators have the group structure of autoequivalences. The Thouless pump operators, together with Hamiltonians with gapped ground states, are then used to construct Floquet drives. An analytic solution for the Floquet phase diagram characterized by winding numbers is constructed when the Floquet drives obey an Onsager algebra. Our approach points the way to a general connection between distinct Thouless pumps and distinct families of Floquet phases.

cond-mat.str-el↗

arXiv2025

Duality defect in a deformed transverse-field Ising model

Physical quantities with long lifetimes have both theoretical significance in the study of quantum many-body systems and practical implications for quantum technologies. In this manuscript, we investigate the roles played by topological defects in the construction of quasi-conserved quantities, using as a prototypical example the Kramers-Wannier duality defect in a deformed 1d quantum transverse field Ising model. We construct the duality defect Hamiltonian in three different ways: half-chain Kramers-Wannier transformation, utilization of techniques in the Ising fusion category, and defect-modified weak integrability breaking deformation. The third method is also applicable for the study of generic integrable defects under weak integrability breaking deformations. We also work out the deformation of defect-modified higher charges in the model and study their slower decay behavior. Furthermore, we consider the corresponding duality defect twisted deformed Floquet transverse field Ising model, and investigate the stability of the isolated zero mode associated with the duality defect in the integrable Floquet Ising model, under such weak integrability breaking deformation.

cond-mat.str-el↗

arXiv2025

Almost Strong Zero Modes at Finite Temperature

Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding non-integrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called Almost Strong Zero Modes, which are long-lived with respect to any bulk excitations. Here, we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature $β$, and on an effective energy scale $Δ_{\rm eff}$ that is greater than the thermodynamic gap of the system $Δ$.

cond-mat.str-el↗

arXiv2025

Disorder induced topological phase transition in a driven Majorana chain

We study a periodically driven one dimensional Kitaev model in the presence of disorder. In the clean limit our model exhibits four topological phases corresponding to the existence or non-existence of edge modes at zero and pi quasienergy. When disorder is added, the system parameters get renormalized and the system may exhibit a topological phase transition. When starting from the Majorana $π$ Mode (MPM) phase, which hosts only edge Majoranas with quasienergy pi, disorder induces a transition into a neighboring phase with both pi and zero modes on the edges. We characterize the disordered system using (i) exact diagonalization (ii) Arnoldi mapping onto an effective tight binding chain and (iii) topological entanglement entropy.

cond-mat.supr-con↗

arXiv2025

Moment method and continued fraction expansion in Floquet Operator Krylov Space

Recursion methods such as Krylov techniques map complex dynamics to an effective non-interacting problem in one dimension. For example, the operator Krylov space for Floquet dynamics can be mapped to the dynamics of an edge operator of the one-dimensional Floquet inhomogeneous transverse field Ising model (ITFIM), where the latter, after a Jordan-Wigner transformation, is a Floquet model of non-interacting Majorana fermions, and the couplings correspond to Krylov angles. We present an application of this showing that a moment method exists where given an autocorrelation function, one can construct the corresponding Krylov angles, and from that the corresponding Floquet-ITFIM. Consequently, when no solutions for the Krylov angles are obtained, it indicates that the autocorrelation is not generated by unitary dynamics. We highlight this by studying certain special cases: stable $m$-periodic dynamics derived using the method of continued fractions, exponentially decaying and power-law decaying stroboscopic dynamics. Remarkably, our examples of stable $m$-periodic dynamics correspond to $m$-period edge modes for the Floquet-ITFIM where deep in the chain, the couplings correspond to a critical phase. Our results pave the way to engineer Floquet systems with desired properties of edge modes and also provide examples of persistent edge modes in gapless Floquet systems.

cond-mat.str-el↗

arXiv2025

Light-induced anomalous Hall conductivity in massive 3D Dirac semimetal Co$_3$Sn$_2$S$_2$

Weyl semimetals can emerge from Dirac semimetals when the time-reversal or spatial-inversion symmetries are broken. Recently, it has been proposed based on the Floquet theory that Dirac semimetals can be converted into Weyl semimetals even by shining circularly polarized light (CPL). Here we have investigated the possibility of such a Dirac-Weyl conversion by measuring the CPL-induced anomalous Hall conductivity (AHC) in a massive 3D Dirac semimetal Co$_3$Sn$_2$S$_2$ in the paramagnetic phase using ultrafast mid-infrared pump-terahertz Faraday rotation probe spectroscopy. We find that the field-strength and driving frequency dependence of the observed AHC is well accounted for by CPL-induced nonzero Berry curvature associated with the splitting of the Dirac bands as predicted by the Floquet theory. The estimated splitting of the Dirac bands reaches about 60 % of the mass gap and the calculated CPL-induced AHC quantitatively reproduces the experimental observation, demonstrating a promising route toward the realization of Floquet-Weyl states from massive Dirac semimetals.

cond-mat.mes-hall↗

arXiv2024

Gapless Floquet topology

Symmetry-protected topological (SPT) phases in insulators and superconductors are known for their robust edge modes, linked to bulk invariants through the bulk-boundary correspondence. While this principle traditionally applies to gapped phases, recent advances have extended it to gapless systems, where topological edge states persist even in the absence of a bulk gap. We extend this framework to periodically driven chains with chiral symmetry, revealing the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. By examining the half-period decomposition of chiral evolutions, we construct topological invariants that circumvent the need to define the Floquet Hamiltonian, making them more suitable for generalization to the gapless regime. We provide explicit examples, including generalizations of the Kitaev chain and related spin models, where localized pi-modes emerge even when the bulk is gapless at the same quasi-energy as the edge modes. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.

cond-mat.str-el↗

arXiv2024

A Universal Model of Floquet Operator Krylov Space

It is shown that the stroboscopic time-evolution under a Floquet unitary, in any spatial dimension, and of any Hermitian operator, can be mapped to an operator Krylov space which is identical to that generated by the edge operator of the non-interacting Floquet transverse-field Ising model (TFIM) in one-spatial dimension, and with inhomogeneous Ising and transverse field couplings. The latter has four topological phases reflected by the absence (topologically trivial) or presence (topologically non-trivial) of edge modes at $0$ and/or $π$ quasi-energies. It is shown that the Floquet dynamics share certain universal features characterized by how the Krylov parameters vary in the topological phase diagram of the Floquet TFIM with homogeneous couplings. These results are highlighted through examples, all chosen for numerical convenience to be in one spatial dimension: non-integrable Floquet spin $1/2$ chains and Floquet $Z_3$ clock model where the latter hosts period-tripled edge modes.

cond-mat.str-el↗

arXiv2024

Floquet Product Mode

Results are presented for the dynamics of edge modes in interacting Floquet Ising chains. It is shown that in addition to the quasi-stable $0$ and $π$ edge modes, a third long lived edge mode arising from the operator product of the $0$ and $π$ edge modes exists. Depending on the microscopic parameters, this Floquet product mode is shown to have a substantially longer lifetime than the individual $0$ and $π$ modes. This is triggered by a scattering process which converts a $0$ mode into a $π$ mode while scattering two bulk excitations. This process can lead to a rapid decay of both $0$ and $π$ mode without affecting the product mode.

cond-mat.str-el↗

arXiv2024

Strong zero modes in integrable quantum circuits

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this work, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

cond-mat.stat-mech↗

arXiv2024

Topological Defects in Floquet Circuits

We introduce a Floquet circuit describing the driven Ising chain with topological defects. The corresponding gates include a defect that flips spins as well as the duality defect that explicitly implements the Kramers-Wannier duality transformation. The Floquet unitary evolution operator commutes with such defects, but the duality defect is not unitary, as it projects out half the states. We give two applications of these defects. One is to analyze the return amplitudes in the presence of "space-like" defects stretching around the system. We verify explicitly that the return amplitudes are in agreement with the fusion rules of the defects. The second application is to study unitary evolution in the presence of "time-like" defects that implement anti-periodic and duality-twisted boundary conditions. We show that a single unpaired localized Majorana zero mode appears in the latter case. We explicitly construct this operator, which acts as a symmetry of this Floquet circuit. We also present analytic expressions for the entanglement entropy after a single time step for a system of a few sites, for all of the above defect configurations.

cond-mat.str-el↗

arXiv2023

Kinetics of information scrambling in correlated electrons: disorder-driven transition from shock-wave to FKPP dynamics

Quenched disorder slows down the scrambling of quantum information. Using a bottom-up approach, we formulate a kinetic theory of scrambling in a correlated metal near a superconducting transition, following the scrambling dynamics as the impurity scattering rate is increased. Within this framework, we rigorously show that the butterfly velocity $v$ is bounded by the light cone velocity $v_{\rm lc }$ set by the Fermi velocity. We analytically identify a disorder-driven dynamical transition occurring at small but finite disorder strength between a spreading of information characterized at late times by a discontinuous shock wave propagating at the maximum velocity $v_{\rm lc}$, and a smooth traveling wave belonging to the Fisher or Kolmogorov-Petrovsky-Piskunov (FKPP) class and propagating at a slower, if not considerably slower, velocity $v$. In the diffusive regime, we establish the relation $v^2/λ_{\rm FKPP} \sim D_{\rm el}$ where $λ_{\rm FKPP}$ is the Lyapunov exponent set by the inelastic scattering rate and $D_{\rm el}$ is the elastic diffusion constant.

cond-mat.stat-mech↗