arXiv subjects

Dganit Meidan

Publications and source records attributed to Dganit Meidan.

At least 19 recordsLinked to original sources

arXiv2025

Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices

Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by the competition between unitary dynamics and dissipation. In this work, we reveal the fundamental role of conservation laws in shaping this competition. Focusing on translation-invariant non-interacting fermionic models with U(1) symmetry, we present a theoretical framework to understand the structure of the steady-state of these models and their entanglement content based on two ingredients: the nature of the spectrum of the non-Hermitian Hamiltonian and the constraints imposed on the steady-state single-particle occupation by the conserved quantities. These emerge from an interplay between Hamiltonian symmetries and initial state, due to the non-linearity of measurement back-action. For models with complex energy spectrum, we show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue. As a result, one can have partially filled or fully filled bands in the steady-state, leading to an entanglement entropy undergoing a filling-driven transition between critical sub volume scaling and area-law, similar to ground-state problems. Conversely, when the spectrum is fully real, we provide evidence that local observables can be captured using a diagonal ensemble, and the entanglement entropy exhibits a volume-law scaling independently on the initial state, akin to unitary dynamics. We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model, uncovering a rich interplay between the single-particle spectrum and conservation laws in determining the steady-state structure and the entanglement transitions. These conclusions are supported by exact analytical calculations and numerical calculations relying on the Faber polynomial method.

cond-mat.stat-mech↗

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

Controlling measurement-induced phase transitions with tunable detector coupling

We study the evolution of a quantum many-body system driven by two competing measurements, which induces a topological entanglement transition between two distinct area law phases. We employ a positive operator-valued measurement with variable coupling between the system and detector within free fermion dynamics. This approach allows us to continuously track the universal properties of the transition between projective and continuous monitoring. Our findings suggest that the percolation universality of the transition in the projective limit is unstable when the system-detector coupling is reduced.

quant-ph↗

arXiv2024

Josephson Junction of Nodal Superconductors with Rashba and Ising Spin-Orbit coupling

We study the effect of a Rashba spin-orbit coupling on the nodal superconducting phase of an Ising superconductor. Such nodal phase was predicted to occur when applying an in-plane field beyond the Pauli limit to a superconducting monolayer transition metal dichalcogenides (TMD). Generically, Rashba spin-orbit is known to lift the chiral symmetry that protects the nodal points, resulting in a fully gapped phase. However, when the magnetic field is applied along the $Γ-K $ line, a residual vertical mirror symmetry protects a nodal crystalline phase. We study a single-band tight-binding model that captures the low energy physics around the $Γ$ pocket of monolayer TMD. We calculate the topological properties, the edge state structure, and the current phase relation in a Josephson junction geometry of the nodal crystalline phase. We show that while the nodal crystalline phase is characterized by localized edge modes on non-self-reflecting boundaries, the current phase relation exhibits a trivial $2π$ periodicity in the presence of Rashba spin-orbit coupling.

cond-mat.mes-hall↗

arXiv2023

Theory of free fermions dynamics under partial post-selected monitoring

Monitored quantum systems undergo Measurement-induced Phase Transitions (MiPTs) stemming from the interplay between measurements and unitary dynamics. When the detector readout is post-selected to match a given value, the dynamics is generated by a Non-Hermitian Hamiltonian with MiPTs characterized by different universal features. Here, we derive a partial post-selected stochastic Schrödinger equation based on a microscopic description of continuous weak measurement. This formalism connects the monitored and post-selected dynamics to a broader family of stochastic evolution. We apply the formalism to a chain of free fermions subject to partial post-selected monitoring of local fermion parities. Within a 2-replica approach, we obtained an effective bosonized Hamiltonian in the strong post-selected limit. Using a renormalization group analysis, we find that the universality of the non-Hermitian MiPT is stable against a finite (weak) amount of stochasticity. We further show that the passage to the monitored universality occurs abruptly at finite partial post-selection, which we confirm from the numerical finite size scaling of the MiPT. Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories and provides a potential route to tackle the experimental post-selected problem.

quant-ph↗

arXiv2022

Topological transitions with continuously monitored free fermions

We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases of distinct topological order. We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. In the presence of unitary dynamics, the two topologically distinct phases are separated by a region with sub-volume scaling of the entanglement entropy. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy. We further show that the phase diagram is qualitatively captured by an analytically tractable non-Hermitian model obtained via post-selecting the measurement outcome. Finally we introduce a partial-post-selection continuous mapping, that uniquely associates topological indices of the non-Hermitian Hamiltonian to the distinct phases of the stochastic measurement-induced dynamics.

quant-ph↗

arXiv2022

Josephson junctions of topological nodal superconductors

Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal superconductivity is associated with an energy-phase relation that depends on the momentum transverse to the current direction, with a $4π$ periodicity in between pairs of nodal points. We interpret this response as a result of a series of quantum phase transitions, driven by the transverse momentum, which separate a topological trivial phase and two distinct topologically non-trivial phases characterized by different winding invariants. This analysis sheds light on the stability of the Majorana flat bands to symmetry-breaking perturbations.

cond-mat.supr-con↗

arXiv2021

Relation between scattering matrix topological invariants and conductance in Floquet Majorana systems

We analyze the conductance of a one-dimensional topological superconductor periodically driven to host Floquet Majorana zero-modes for different configurations of coupling to external leads. We compare the conductance of constantly coupled leads, as in standard transport experiments, with the stroboscopic conductance of pulsed coupling to leads used to identify a scattering matrix topological index for periodically driven systems. We find that the sum of DC conductance at voltages multiples of the driving frequency is quantitatively close to the stroboscopic conductance at all voltage biases. This is consistent with previous work which indicated that the summed conductance at zero/pi resonance is quantized. We quantify the difference between the two in terms of the width of their respective resonances and analyze that difference for two different stroboscopic driving protocols of the Kitaev chain. While the quantitative differences are protocol-dependent, we find that generically the discrepancy is larger when the zero mode weight at the end of the chain depends strongly on the offset time between the driving cycle and the pulsed coupling period.

cond-mat.mes-hall↗

arXiv2020

Pumped heat and charge statistics from Majorana braiding

We examine the heat and charge transport of a driven topological superconductor. Our particular system of interest consists of a Y-junction of topological superconducting wires, hosting non-Abelian Majorana zero modes at their edges. The system is contacted to two leads which act as continuous detectors of the system state. We calculate, via a scattering matrix approach, the full counting statistics of the driven heat transport, between two terminals contacted to the system, for small adiabatic driving and characterise the energy transport properties as a function of the system parameters (driving frequency, temperature). We find that the geometric, dynamic contribution to the pumped heat statistics results in a correction to the Gallavotti-Cohen type fluctuation theorem for quantum heat transfer. Notably, the correction term to the fluctuation theorem extends to cycles which correspond to topologically protected braiding of the Majorana zero modes. This geometric correction to the fluctuation theorem differs from its analogs in previously studied systems in that (i) it is non-vanishing for adiabatic cycles of the system's parameters, without the need for cyclic driving of the leads and (ii) it is insensitive to small, slow fluctuations of the driving parameters due to the topological protection of the braiding operation.

cond-mat.mes-hall↗

arXiv2020

Constrained thermalisation and topological superconductivity

We examine the thermalisation/localization trade off in an interacting and disordered Kitaev model, specifically addressing whether signatures of many-body localization can coexist with the systems topological phase. Using methods applicable to finite size systems, (e.g. the generalized one-particle density matrix, eigenstate entanglement entropy, inverse zero modes coherence length) we identify a regime of parameter space in the vicinity of the non-interacting limit where topological superconductivity survives together with a significant violation of Eigenstate-Thermalisation-Hypothesis (ETH) at finite energy-densities. We further identify an anomalous behaviour of the von Neumann entanglement entropy which can be attributed to the prethermalisation-like effects that occur due to lack of hybridization between high-energy eigenstates reflecting an approximate particle conservation law. In this regime the system tends to thermalise to a generalised Gibbs ensemble (as opposed to the grand canonical ensemble). Moderate disorder tends to drive the system towards stronger hybridization and a standard thermal ensemble, where the approximate conservation law is violated. This behaviour is cutoff by strong disorder which obstructs many body effects thus violating ETH and reducing the entanglement entropy.

cond-mat.str-el↗

arXiv2018

Topologically protected heat pumping from braiding Majorana zero modes

Majorana zero modes are non-Abelian quasiparticles that emerge on the edges of topological phases of superconductors. Evidence of their presence has been reported in transport measurements on engineered superconducting-based nanostructures. In this manuscript we identify signatures of a topologically protected dynamical manipulation of Majorana zero modes via continuous transport measurement during the manipulation. Specifically, we show that, in a two-terminal geometry, the heat pumped across the terminals at low temperature and voltage bias is characterized by a universal value. We show that this feature is inherent to the presence of Majorana zero modes and discuss its robustness against temperature, voltage bias and the detailed coupling to the contacts.

cond-mat.mes-hall↗

arXiv2018

Localization due to topological stochastic disorder in active networks

An active network is a prototype model in non-equilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle, and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations; or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergent aspect is the topological stochastic disorder (TSD). It is implied by the non-uniformity of the illumination. In technical terms the TSD reflects the local non-zero circulations (affinities) of the stochastic transitions. This type of disorder, unlike non-homogeneous magnetic field, is non-hermitian, and can lead to the emergence of a complex relaxation spectrum. It is therefore dramatically distinct from the conservative Anderson-type or Sinai-type disorder. We discuss the consequences of having TSD. In particular we illuminate 3~different routes to under-damped relaxation, and show that localization plays a major role in the analysis. Implications of the bulk-edge correspondence principle are addressed too.

cond-mat.stat-mech↗

arXiv2018

Localization-enhanced and degraded topological-order in interacting p-wave wires

We numerically study the effect of disorder on the stability of the many body zero mode in a Kitaev chain with local interactions. Our numerical procedure allows us to resolve the position-space and multi-particle structure of the zero modes, as well as providing estimates for the mean energy splitting between pairs of states of opposite fermion parity, over the full many-body spectrum. We find that the parameter space of a clean system can be divided into regions where interaction induced decay transitions are suppressed (Region I) and where they are not (Region II). In Region I we observe that disorder has an adverse effect on the zero mode, which extends further into the bulk and is accompanied by an increased energy splitting between pairs of states of opposite parity. Conversely Region II sees a more intricate effect of disorder, showing an enhancement of localization at the system's end accompanied by a reduction in the mean pairwise energy splitting. We discuss our results in the context of the Many-Body Localization (MBL). We show that while the mechanism that drives the MBL transition also contributes to the fock-space localization of the many-body zero modes, measures that characterize the degree of MBL do not necessarily correlate with an enhancement of the zero-mode or an improved stability of the topological region.

cond-mat.str-el↗

arXiv2017

Transport properties of an interacting Majorana chain

We study a one-dimensional (1D) chain of $2N$ Majorana bound states, which interact through a local quartic interaction. This model describes for example the edge physics of a quasi 1D stack of $2N$ Kitaev chains with modified time-reversal symmetry $Tγ_iT^{-1}=γ_i$, which precludes the presence of quadratic coupling. The ground state of our 1D Majorana chain displays a four-fold periodicity in $N$, corresponding to the four distinct topological classes of the stacked Kitaev chains. We analyze the transport properties of the 1D Majorana chain, when probed by local conductors located at its ends. We find that for finite but large $N$, the scattering matrix partially reflects the four-fold periodicity, and the chain exhibits strikingly different transport properties for different chain lengths. In the thermodynamic limit, the 1D Majorana chain hosts a robust many-body zero mode, which indicates that the corresponding stacked two-dimensional bulk system realizes a weak topological phase.

cond-mat.mes-hall↗

arXiv2015

Transport signatures of interacting fermions in quasi-one-dimensional topological superconductors

A topological superconducting wire with an effective time reversal symmetry is known to have a $\mathbb{Z}_8$ topological classification in the presence of interactions. The topological index $|n| \le 4$ counts the number of Majorana end states, negative $n$ corresponding to end states that are odd under time reversal. If such a wire is weakly coupled to a normal-metal lead, interactions induce a Kondo-like correlated state if $|n| = 4$. We show that the Kondo-like state manifests itself in an anomalous temperature dependence of the zero-bias conductance and by an anomalous Fano factor for the zero-temperature normally-reflected current at finite bias. We also consider the splitting of the effective Kondo resonance for weak symmetry-breaking perturbations.

cond-mat.mes-hall↗

arXiv2013

A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors

We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time reversal symmetry in the presence of interactions. For a closed geometry, Fidkowski and Kitaev have shown that such systems have a $\mathbb{Z}_8$ topological classification. We show that in the weak coupling limit, these systems retain a unitary scattering matrix at zero temperature, with a topological index given by the trace of the Andreev reflection matrix, $\mbox{tr}\, r_{\rm he}$. With interactions, $\mbox{tr}\, r_{\rm he}$ generically takes on the finite set of values $0$, $\pm 1$, $\pm 2$, $\pm 3$, and $\pm 4$. We show that the two topologically equivalent phases with $\mbox{tr}\, r_{\rm he} = \pm 4$ support emergent many-body end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.

cond-mat.mes-hall↗

arXiv2011

Gapless excitations in strongly fluctuating superconducting wires

We study the low temperature tunneling density of states of thin wires where superconductivity is destroyed through quantum phase-slip proliferation. Although this regime is believed to behave as an insulator, we show that for a large temperature range this phase is characterized by a conductivity falling off at most linearly with temperature, and has a gapless excitation spectrum. This novel conducting phase results from electron-electron interaction induced pair breaking. Also, it may help clarify the low temperature metallic features found in films and wires whose bulk realization is superconducting.

cond-mat.mes-hall↗

arXiv2011

Topological classification of adiabatic processes

Certain band insulators allow for the adiabatic pumping of quantized charge or spin for special time-dependences of the Hamiltonian. These "topological pumps" are closely related to two dimensional topological insulating phases of matter upon rolling the insulator up to a cylinder and threading it with a time dependent flux. In this article we extend the classification of topological pumps to the Wigner Dyson and chiral classes, coupled to multi-channel leads. The topological index distinguishing different topological classes is formulated in terms of the scattering matrix of the system. We argue that similar to topologically non-trivial insulators, topological pumps are characterized by the appearance of protected gapless end states during the course of a pumping cycle. We show that this property allows for the pumping of quantized charge or spin in the weak coupling limit. Our results may also be applied to two dimensional topological insulators, where they give a physically transparent interpretation of the topologically non-trivial phases in terms of scattering matrices.

cond-mat.mes-hall↗