arXiv subjects

Alexander D. Mirlin

Publications and source records attributed to Alexander D. Mirlin.

At least 19 recordsLinked to original sources

arXiv2026

Signatures of localization on the edge of a fractional topological insulator

Recent experiments in van der Waals moiré materials have reported realizations of two-dimensional fractional topological insulators (FTIs). We study transport properties of FTI edges at filling factors $ν_{\text{FTI}} = 2(1\pm 1/n)$ with integer $n \geq 2$ (even or odd), each of which supports four counter-propagating edge modes. The edge modes can undergo partial localization, leaving two of the four edge modes conducting. We identify three distinct partial-localization channels and, for each channel, determine the reduced theory describing the remaining conducting modes, from which we obtain the minimal quasiparticle charge. We further explore transport properties of each partially localized phase and in particular determine the corresponding edge conductances. We demonstrate that measurements of the conductance together with the minimal quasiparticle charge provide a fingerprint that uniquely distinguishes the three partially localized phases.

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arXiv2026

Monitored free fermions under periodic driving

We investigate analytically and numerically a one-dimensional periodically driven free-fermionic system subjected to monitoring of the local particle density. Based on the analytical approach that describes the long-wavelength physics of the time-dependent Hamiltonian in the field-theoretical language using the nonlinear sigma-model (NLSM), we reveal that driving does not alter the universality class of the problem. As a consequence, the system retains the area-law behavior in the thermodynamic limit, with an intermediate diffusive regime giving rise to logarithmic growth of entanglement entropy for a small monitoring rate. At the same time, driving leads to a renormalization of the bare coupling constant of the NLSM, which controls the space-time ``conductivity'' in the diffusive regime. We derive the analytic form of this renormalization, which becomes particularly strong in the case of a ``maximally symmetric'' drive and sufficiently short driving period. In addition, we employ the Wiener-Hopf method to investigate the ballistic-diffusive crossover. These analytical predictions are corroborated by numerical simulations of the von-Neumann entanglement entropy and the density correlation function. Our numerical results clearly demonstrate that, with an increase in the system size, there are successive crossovers from ballistic to diffusive behavior and ultimately to localization. Furthermore, in the diffusive regime, we observe weak-localization corrections that are in agreement with the analytical predictions of the NLSM. Overall, our results provide a unified analytical and numerical framework for understanding the effects of monitoring in time-modulated fermionic systems, paving a way for broader investigations of driven quantum matter.

cond-mat.dis-nn↗

arXiv2026

Non-equilibrium bosonization of fractional quantum Hall edges

Edge transport serves as a powerful probe of remarkable low-energy properties of fractional quantum Hall states, including the anyonic character of their excitations. Here, we develop a theory of fractional quantum Hall edges driven out of equilibrium, which is based on the Keldysh action for the bosonized chiral Luttinger liquid. With this non-equilibrium FQH bosonization framework, we first consider a single-mode Laughlin edge and analyze the full counting statistics of charge, the quasiparticle Green's functions, and tunneling transport properties through a quantum point contact, allowing for generic edge excitations. We then extend the formalism to multi-mode edges with inter-mode interactions, and explore, with focus on the $ν=4/3$ and $ν=2/3$ edges as paradigmatic examples, how interaction-induced fractionalization of anyons modifies the edge dynamics and the associated transport observables. While the full counting statistics probes the fractionalized charge of the excitations, the Green's functions and tunneling transport are governed by mutual braiding phases of fractionalized excitations and tunneling quasiparticles. We emphasize in particular the effect of interaction-induced fractionalization on the Fano factor $F$ and the differential Fano factor $F_d$, observables that can be measured experimentally. Our formalism, which provides a unified framework for non-equilibrium transport in FQH edges and Luttinger liquids, permits extracting anyonic braiding information from non-equilibrium edge-transport experiments, and paves the way to various extensions, including more involved experimental geometries and edge structures.

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arXiv2026

Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition

We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case of finite evolution time $T$ and different classes of initial states, which lead to different NLSM boundary conditions. The analytical formalism is then used to study how quantum correlations gradually develop, with increasing $T$, from those determined by the initial state towards their steady-state form. The analytical results are confirmed by numerical simulations for several types of initial states. We further consider the long-time limit, when the system in $d+1$ space-time dimensions becomes quasi-one-dimensional, and analyze the scaling of the ``localization'' time (which is simultaneously the purification time and the charge-sharpening time for this class of problems). The analytical predictions for scaling properties are fully confirmed by numerical simulations in a $d=2$ model around the measurement-induced phase transition. We use this dynamical approach to determine numerically the measurement-induced transition point and the associated correlation-length critical exponent.

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arXiv2025

Measurement-induced Lévy flights of quantum information

We explore a model of free fermions in one dimension, subject to frustrated (non-commuting) local measurements across adjacent sites, which resolves the fermions into non-orthogonal orbitals, misaligned from the underlying lattice. For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate at one point in the Brillouin zone, which generates fractal-scaling entanglement entropy $S \propto \ell^{1/3}$ for a subsystem of length $\ell$. We derive an effective non-linear sigma model with long-range couplings responsible for Lévy flights in entanglement propagation, which we confirm with large-scale numerical simulations. When the misalignment is reduced, the entanglement exhibits, with increasing $\ell$, consecutive regimes of superdiffusive, $S\propto \ell^{1/3}$, diffusive, $S\propto \ln \ell$, and localized, $S = \rm{const}$, behavior. Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians and measurements.

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arXiv2025

Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition

We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are the particle-number covariance between spatially separated regions, $G_{AB}$, and the two-point density correlation function, $\mathcal{C}(r)$. Our results exhibit a remarkable analogy to Anderson localization, with $G_{AB}$ corresponding to two-terminal conductance and $\mathcal{C}(r)$ to two-point conductance, albeit with different replica limit and unconventional symmetry class, geometry, and boundary conditions. In the delocalized phase, $G_{AB}$ exhibits ``universal'', nearly Gaussian, fluctuations with variance of order unity. In the localized phase, we find a broad distribution of $G_{AB}$ with $\overline{-\ln G_{AB}} \sim L $ (where $L$ is the system size) and the variance $\mathrm{var}(\ln G_{AB}) \sim L^μ$, and similarly for $\mathcal{C}(r)$, with $μ\approx 0.5$. At the transition point, the distribution function of $G_{AB}$ becomes scale-invariant and $\mathcal{C}(r)$ exhibits multifractal statistics, $\overline{\mathcal{C}^{q}(r)}\sim r^{-q(d+1) - Δ_{q}}$. We characterize the spectrum of multifractal dimensions $Δ_q$. Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.

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arXiv2025

Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space

Many-body-localization (MBL) transitions are studied in a family of single-spin-flip spin-$\frac12$ models, including the one-dimensional (1D) chain with nearest-neighbor interactions, the quantum dot (QD) model with all-to-all pair interactions, and the quantum random energy model (QREM). We investigate the generalized imbalance that characterizes propagation in Fock space out of an initial basis state and, at the same time, can be efficiently probed by real-space measurements. For all models considered, the average imbalance and its quantum and mesoscopic fluctuations provide excellent indicators for the position of the MBL transition $W_c(n)$, where $n$ is the number of spins. Combining these findings with earlier results on level statistics, we determine phase diagrams of the MBL transitions in the $n$-$W$ plane. Our results provide evidence for a direct transition between the ergodic and MBL phases for each of the models, without any intermediate phase. For QREM and QD model, $W_c(n)$ grows as a power law of $n$ (with logarithmic corrections), in agreement with analytical predictions $W_c^{\rm QREM}(n) \sim n^{1/2} \ln n$ and $W_c^{\rm QD}(n) \gtrsim n^{3/4} \ln^{1/2} n$. This growth is in stark contrast to the 1D model, where $W_c(n)$ is essentially independent of $n$, consistent with the analytic expectation $W_c^{\rm 1D}(n\to \infty)= {\rm const}$. We also determine the scaling of the transition width $ΔW (n) / W_c(n)$ and estimate the system size $n$ needed to study the asymptotic scaling behavior. While these values of $n$ are not accessible to exact simulations on a classical computer, they are within the reach of quantum simulators. Our results indicate feasibility of experimental studies of $n$-$W$ phase diagrams and scaling properties of MBL transitions in models of 1D and QD type and in their extensions to other spatial geometry or distance-dependent interactions.

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arXiv2025

Measurement-induced transitions for interacting fermions

Effect of measurements on interacting fermionic systems with particle-number conservation, whose dynamics is governed by a time-independent Hamiltonian, is studied. We develop Keldysh field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM), which incorporates boundary conditions specifically designed to produce generating functions for charge cumulants and entanglement entropies directly in the NLSM language. By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables. Crucially, the interaction-induced terms in the NLSM action reduce its symmetry, which affects the physics of the problem in a dramatic way. First, this leads to the "information-charge separation": charge cumulants get decoupled from entanglement entropies. Second, the interaction stabilizes the volume-law phase for the entanglement. Third, for spatial dimensionality $d=1$, the interaction stabilizes the phase with logarithmic growth of charge cumulants (in the thermodynamic limit). Thus, in the presence of interaction, there are measurement transitions in any $d$, at variance with free fermions, for which a $d=1$ system is always in the area-law phase. Analytical results are supported by numerical simulations using time-dependent variational principles for matrix product states, which, in particular, confirm the separation of information and charge as a hallmark of the delocalized phase.

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arXiv2024

Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions

A junction of two 2/3 fractional quantum Hall (FQH) edges, with no charge tunneling between them, may exhibit Anderson localization of neutral modes. Manifestations of such localization in transport properties of the junction are explored. There are two competing localization channels, ``neutral-mode superconductivity'' and ``neutral-mode backscattering''. Localization in any of these channels leads to an effective theory of the junction that is characteristic for FQH effect of bosons, with a minimal integer excitation charge equal to two, and with elementary quasiparticle charge equal to 2/3. These values can be measured by studying shot noise in tunneling experiments. Under the assumption of ballistic transport in the arms connecting the junction to contacts, the two-terminal conductance of the junction is found to be 4/3 for the former localization channel and 1/3 for the latter. The four-terminal conductance matrix reveals in this regime a strong quantized drag between the edges induced by neutral-mode localization. The two localization channels lead to opposite signs of the drag conductance, equal to $\pm 1/4$, which can also be interpreted as a special type of Andreev scattering. Coherent random tunneling in arms of the device (which are segments of 2/3 edges) leads to strong mesoscopic fluctuations of the conductance matrix. In the case of fully equilibrated arms, transport via the junction is insensitive to neutral-mode localization: The two-terminal conductance is quantized to 2/3 and the drag is absent.

cond-mat.mes-hall↗

arXiv2024

Role of Fock-space correlations in many-body localization

Models of many-body localization (MBL) can be represented as tight-binding models in the many-body Hilbert space (Fock space). We explore the role of correlations between matrix elements of the effective Fock-space Hamiltonians in the scaling of MBL critical disorder $W_c(n)$ with the size $n$ of the system. For this purpose, we consider five models, which all have the same distributions of diagonal (energy) and off-diagonal ("hopping") Fock-space matrix elements but different Fock-space correlations. These include quantum-dot (QD) and one-dimensional (1D) MBL models, their modifications (uQD and u1D models) with removed correlations of off-diagonal matrix elements, as well a quantum random energy model (QREM) with no correlations at all. Our numerical results are in full consistency with analytical arguments predicting $n^{3/4} (\ln n)^{-1/4} \lesssim W_c \lesssim n \ln n$ for the scaling of $W_c(n)$ in the QD model (we find $W_c \sim n$ numerically), $W_c(n) \sim \text{const.}$ for the 1D model, $W_c \sim n \ln n$ for the uQD and u1D models without off-diagonal correlations, and $W_c \sim n^{1/2} \ln n$ for QREM. The key difference between the QD and 1D models is in the structure of correlations of many-body energies. Removing off-diagonal Fock-space correlations makes both these models "maximally chaotic". Our findings demonstrate that the scaling of $W_c(n)$ for MBL transitions is governed by a combined effect of Fock-space correlations of diagonal and off-diagonal matrix elements.

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arXiv2024

Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors

We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (``detectors''), which are periodically measured by means of strong projective measurements. The concentration $ρ_a$ of ancillae and their coupling $M$ to the main system are considered as parameters. We explore the dynamics of density and of entanglement entropy in the chain, for various values of $ρ_a$ and $M$ for two models of the detector-chain interaction that couple the local density in the chain to a detector degree of freedom. It is found that, for the density-density ($S_z s_z$-type in spin language) coupling, the critical values $M_c$ for the measurement-induced entanglement transition depends sensitively on $ρ_a$. Moreover, our results indicate that for a sufficiently small $ρ_a$ the transition in this model disappears, i.e., a finite density of detectors is needed to reach a disentangling phase. The behavior is qualitatively different for the second model, with density-hopping ($S_z s_x$-type) coupling. Specifically, the dynamics is much less sensitive to the concentration $ρ_a$ of detectors than in the first model. Furthermore, the dependence of entanglement on the coupling strength $M$ is strongly non-monotonic, indicating re-entrance of the entangling phase at large $M$.

quant-ph↗

arXiv2024

Localization and conductance in fractional quantum Hall edges

The fractional quantum Hall (FQH) effect gives rise to abundant topological phases, presenting an ultimate platform for studying the transport of edge states. Generic FQH edge contains multiple edge modes, commonly including the counter-propagating ones. A question of the influence of Anderson localization on transport through such edges arises. Recent experimental advances in engineering novel devices with interfaces of different FQH states enable transport measurements of FQH edges and edge junctions also featuring counter-propagating modes. These developments provide an additional strong motivation for the theoretical study of the effects of localization on generic edge states. We develop a general framework for analyzing transport in various regimes that also naturally includes localization. Using a reduced field theory of the edge after localization, we derive a general formula for the conductance. We apply this framework to analyze various experimentally relevant geometries of FQH edges and edge junctions.

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arXiv2024

Measurement-induced phase transition for free fermions above one dimension

A theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. The critical point separates a gapless phase with $\ell^{d-1} \ln \ell$ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with $\ell^{d-1}$ scaling, where $\ell$ is a size of the subsystem. The problem is mapped onto an SU($R$) replica non-linear sigma model in $d+1$ dimensions, with $R\to 1$. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for $d = 1+ ε$ with $ε\ll 1$. Further, we carry out a numerical study of the transition for a $d=2$ model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, $ν\approx 1.4$.

quant-ph↗

arXiv2024

Fingerprints of anti-Pfaffian topological order in quantum point contact transport

Despite recent experimental developments, the topological order of the fractional quantum Hall state at filling $ν=5/2$ remains an outstanding question. We study conductance and shot noise in a quantum point contact device in the charge-equilibrated regime and show that, among Pfaffian, particle-hole Praffian, and anti-Pfaffian (aPf) candidate states, the hole-conjugate aPf state is unique in that it can produce a conductance plateau at $G=(7/3)e^2/h$ by two fundamentally distinct mechanisms. We demonstrate that these mechanisms can be distinguished by shot noise measurements on the plateaus. We also determine distinct features of the conductance of the aPf state in the coherent regime. Our results can be used to experimentally single out the aPf order.

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arXiv2023

Theory of free fermions under random projective measurements

We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, $γ/ J \ll 1$ (where $γ$ is measurement rate per site and $J$ is hopping constant in the tight-binding model), we derive a non-linear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is described by a $U(2) / U(1) \times U(1) \simeq S_2$ sigma model with diffusive behavior, and the replica-asymmetric sector is a two-dimensional NLSM defined on $SU(R)$ manifold with the replica limit $R \to 1$. On the Gaussian level, valid in the limit $γ/ J \to 0$, this model predicts a logarithmic behavior for the second cumulant of number of particles in a subsystem and for the entanglement entropy. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value $\sim (J / γ)^2$ even for rare measurements, which corresponds to the area-law phase. This implies the absence of a measurement-induced entanglement phase transition for free fermions. The crossover between logarithmic growth and saturation, however, happens at exponentially large scale, $\ln l_\text{corr} \sim J / γ$. This makes this crossover very sharp as a function of the measurement frequency $γ/ J$, which can be easily confused with a transition from the logarithmic to area law in finite-size numerical calculations. We have performed a careful numerical analysis, which supports our analytical predictions.

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arXiv2023

Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet

Collective spin-wave excitations-magnons-in a quantum Hall ferromagnet are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. Detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if these signals are equal the magnon detection remains elusive. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is generated by equilibration (partial or full, depending on the bias voltage) between edge channels and propagating magnons. Our model, which agrees with experimental observations, also allows us to pinpoint the regime of ballistic magnon transport in our device.

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arXiv2023

Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots

Anderson localization on random regular graphs (RRG) serves as a toy-model of many-body localization (MBL). We explore the transition for ergodicity to localization on RRG with large connectivity $m$. In the analytical part, we focus on the inverse participation ratio of eigenstates and identify several regimes on the ergodic side of the transition -- self-consistent golden rule, golden rule, precritical, and critical -- that the system consecutively goes through when the disorder increases towards the point $W_c$ of the localization transition. We also perform exact-diagonalization numerics as well as a population-dynamics analysis that combines analytical and numerical techniques. Results of all the approaches are in excellent mutual agreement. We further explore the evolution from ergodicity to localization in two models of Fock-space MBL: fermionic and spin quantum dots. Large-connectivity RRG models serve as an approximation for this class of many-body problems; one of our central goals is to better understand the status of this approximation. Our numerical simulations support the conjecture that, in the limit of a large system, there is a sharp ergodicity-to-localization transition in the quantum-dot models. Furthermore, our results are consistent the RRG-like scaling of the critical disorder, $W_c \sim m \ln m$. While in the golden-rule range the behavior of quantum-dot models is in agreement with analytical predictions based on RRG model, substantial deviations occur in the pre-critical regime. Our results indicate that the pre-critical and critical behavior (as well as the numerical coefficient in the formula for $W_c$) in the quantum-dot models may be different from what one would expect from the RRG-like approximation.

cond-mat.dis-nn↗

arXiv2023

Evolution of many-body systems under ancilla quantum measurements

Measurement-induced phase transitions are the subject of intense current research, both from an experimental and a theoretical perspective. We explore the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom (implemented using two additional sites), on which projective measurements are performed. We analyze the effect of repeated (``stroboscopic'') measurements on the dynamical correlations of interacting hard-core bosons in a one-dimensional chain. An important distinctive ingredient of the protocol is the fact that the detector ancillas are not re-initialized after each measurement step. The detector thus maintains memory of the accumulated influence by the measured correlated system. Initially, we consider a model in which the ancilla is coupled to a single lattice site. This setup allows obtaining information about the system through Rabi oscillations in the ancillary degrees of freedom, modulated by the ancilla-system interaction. The statistics of quantum trajectories exhibits a ``quantum-Zeno-valve effect'' that occurs when the measurement becomes strong, with sharp branching between low and high entanglement. We proceed by extending numerical simulations to the case of two ancillas and, then, to measurements on all sites. With this realistic measurement apparatus, we find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models. The dynamics features a broad distribution of the entanglement entropy.

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