arXiv subjects

Miroslav Hopjan

Publications and source records attributed to Miroslav Hopjan.

At least 19 recordsLinked to original sources

arXiv2026

On spectral properties of Generalized Kadanoff--Baym Ansatz

The Generalized Kadanoff--Baym Ansatz with mean-field propagators is increasingly used to simulate non-equilibrium quantum fermionic and bosonic systems. Compared with the full Kadanoff--Baym equations, its mean-field propagators substantially reduce computational cost, enabling simulations with computational effort that scales linearly with propagation time. However, the time-diagonal structure of the Generalized Kadanoff--Baym Ansatz obscures spectral properties within the collision integral of the transport equation. Here, we recover and investigate these hidden spectral properties using the extended Generalized Kadanoff--Baym Ansatz. For a Hubbard cluster, we compare ground-state spectral functions obtained with the extended Generalized Kadanoff--Baym Ansatz against those from standard Kadanoff--Baym equations. At moderate interaction strengths, the spectral functions show good agreement. At large interaction strengths, however, significant deviations emerge, and the spectral function obtained with the extended Generalized Kadanoff--Baym Ansatz becomes negative. These results demonstrate that, despite its computational advantages, the Generalized Kadanoff--Baym Ansatz has important limitations in strongly interacting regimes and may produce unphysical spectral properties when interactions become sufficiently large.

cond-mat.str-el↗

arXiv2026

Many-body ergodicity breaking from wavefunction snapshots

Modern quantum experiments can probe many-body wavefunctions through projective measurements, providing snapshots of individual many-body configurations. A fundamental question is whether the intrinsic structure of their measurement distributions can reveal quantum dynamics beyond predefined observables. Here, we address this question at the many-body ergodicity-breaking transition using two complementary characteristics of nonequilibrium wavefunction snapshots: their binary intrinsic dimension (BID) and the topology of wavefunction networks constructed from Hamming distances. We show that the critical point is characterized by an extensive but submaximal BID, and scale-free network connectivity with highly connected hubs. These signatures distinguish the ergodic, critical, and nonergodic regimes, and provide experimentally accessible probes of ergodicity breaking from projective measurement snapshots.

quant-ph↗

arXiv2026

Information Compression at Criticality

Highly excited quantum states at the critical boundary of ergodicity are known to deviate from thermal behavior, yet their dynamical properties remain poorly understood. Here, we uncover the complexity of quantum dynamics at criticality through the lens of intrinsic information compression in energy space. We show that the Hamiltonian spectrum can be systematically truncated, yielding a simplified description of the dynamics while preserving its essential features. Specifically, for both interacting and noninteracting systems, we demonstrate that a vanishing fraction of Hamiltonian eigenlevels suffices to reproduce the power-law decay of the survival probability. The resulting truncated spectrum exhibits a fractal structure characterized by a level-spacing distribution with a power-law tail, while its spectral form factor displays the same asymptotic power-law decay as the survival probability.

cond-mat.stat-mech↗

arXiv2026

Computing eigenpairs of quantum many-body systems with Polfed.jl

We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED) algorithm for computing mid-spectrum eigenvalues and eigenvectors (shortly, eigenpairs) of quantum many-body Hamiltonians. Access to such eigenpairs is essential for studying non-equilibrium many-body physics, but is hindered by the exponential growth of Hilbert-space dimension. POLFED addresses this challenge through a polynomial spectral transformation evaluated on the fly within a Lanczos iteration, preserving Hamiltonian sparsity and substantially reducing memory costs compared to other diagonalization methods. The package supports flexible energy targeting, automatic optimization of the spectral mapping for structured Hamiltonians, and GPU acceleration, which is particularly effective since the dominant computational cost reduces to repeated sparse matrix-vector multiplications. Benchmarks on disordered spin-chain and fermionic models demonstrate access to larger system sizes than alternative approaches, and CPU--GPU comparisons confirm significant speedups. In particular, we also provide code for constructing the quantum sun model Hamiltonian, a toy model of a many-body ergodicity-breaking transition. While our focus is on many-body Hamiltonians, Polfed$.$jl may be applied to any large sparse matrix.

cond-mat.stat-mech↗

arXiv2026

Fading ergodicity and quantum dynamics in random matrix ensembles

Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles -- the Rosenzweig-Porter model and the ultrametric model -- fall within the same universality class of ergodicity breaking when embedded in a many-body Hilbert space of spins-1/2. By calibrating the parameters of both models via their Thouless times, we demonstrate that the matrix elements of local observables display similar statistical properties, allowing us to identify the fractal phase of the Rosenzweig-Porter model with the fading-ergodicity regime. This correspondence is further supported through the analyses of quantum-quench dynamics of local observables, their temporal fluctuations and power spectra, and survival probabilities. Our findings reveal that local observables thermalize within the fading-ergodicity regime on timescales shorter than the Heisenberg time, thus providing a unified framework for understanding ergodicity breaking across these distinct models.

cond-mat.stat-mech↗

arXiv2025

Scaling theory of fading ergodicity

In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down for interacting systems that exhibit the many-body ergodicity breaking transition. Here we introduce a scaling theory of fading ergodicity, which is a precursor regime of many-body ergodicity breaking. We argue that the two-parameter scaling governs the entire ergodic regime; however, (i) it evolves into the one-parameter scaling at the ergodicity breaking critical point with the critical exponent $ν=1$, and (ii) it gives rise to the resilient one-parameter scaling close to the ETH point. Our theoretical framework may serve as a building block for two-parameter scaling theories of many-body systems.

cond-mat.stat-mech↗

arXiv2025

Universal Relation between Spectral and Wavefunction Properties at Criticality

Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and their statistics is Poisson. At the boundary between quantum chaos and localization, however, one observes critical behavior, not complying with any of those characteristics. An outstanding open question is whether there exist yet another type of universality, which is genuine for the critical point. Previous work suggested that there may exist a relation between the global characteristics of energy spectrum, such as spectral compressibility $χ$, and the degree of wavefunction delocalization, expressed via the fractal dimension $D_1$ of the Shannon--von Neumann entropy in a preferred (e.g., real-space) basis. Here we study physical systems subject to local and non-local hopping, both with and without time-reversal symmetry, with the Anderson models in dimensions three to five being representatives of the first class, and the banded random matrices as representatives of the second class. Our thorough numerical analysis supports validity of the simple relation $χ+ D_1 = 1$ in all systems under investigation. Hence we conjecture that it represents a universal property of a broad class of critical models. Moreover, we test and confirm the accuracy of our surmise for a closed-form expression of the spectral compressibility in the one-parameter critical manifold of random banded matrices. Based on these findings we derive a universal function $D_{1}(r)$, where $r$ is the averaged level spacing ratio, which is valid for a broad class of critical systems.

cond-mat.stat-mech↗

arXiv2025

Critical Dynamics in Short-Range Quadratic Hamiltonians

We investigate critical transport and the dynamical exponent through the spreading of an initially localized particle in quadratic Hamiltonians with short-range hopping in lattice dimension $d_l$. We consider critical dynamics that emerges when the Thouless time, i.e., the saturation time of the mean-squared displacement, approaches the typical Heisenberg time. We establish a relation, $z=d_l/d_s$, linking the critical dynamical exponent $z$ to $d_l$ and to the spectral fractal dimension $d_s$. This result has notable implications: it says that superdiffusive transport in $d_l\geq 2$ and diffusive transport in $d_l\geq 3$ cannot be critical in the sense defined above. Our findings clarify previous results on disordered and quasiperiodic models and, through Fibonacci potential models in two and three dimensions, provide non-trivial examples of critical dynamics in systems with $d_l\neq1$ and $d_s\neq1$.

cond-mat.stat-mech↗

arXiv2024

Fading ergodicity

Eigenstate thermalization hypothesis (ETH) represents a breakthrough in many-body physics since it allows to link thermalization of physical observables with the applicability of random matrix theory (RMT). Recent years were also extremely fruitful in exploring possible counterexamples to thermalization, ranging, among others, from integrability, single-particle chaos, many-body localization, many-body scars, to Hilbert-space fragmentation. In all these cases the conventional ETH is violated. However, it remains elusive how the conventional ETH breaks down when one approaches the boundaries of ergodicity, and whether the range of validity of the conventional ETH coincides with the validity of RMT-like spectral statistics. Here we bridge this gap and we introduce a scenario of the ETH breakdown in many-body quantum systems, dubbed fading ergodicity regime, which establishes a link between the conventional ETH and non-ergodic behavior. We conjecture this scenario to be relevant for the description of finite many-body systems at the boundaries of ergodicity, and we provide numerical and analytical arguments for its validity in the quantum sun model of ergodicity breaking phase transition. For the latter, we provide evidence that the breakdown of the conventional ETH is not associated with the breakdown of the RMT-like spectral statistics.

cond-mat.stat-mech↗

arXiv2024

Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models

We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to a similar relationship between the non-equal time and space density correlation functions in many-body states and the transition probabilities of single-particle states at nonzero distances. Finally, we study the equal time connected density-density correlation functions in many-body states, which exhibit certain qualitative analogies with the survival and transition probabilities of single-particle states. Our results are numerically tested for two paradigmatic models of single-particle localization: the 3D Anderson model and the 1D Aubry-André model. This work gives affirmative answer to the question whether it is possible to measure features of the single-particle survival and transition probabilities by the dynamics of observables in many-body states.

cond-mat.stat-mech↗

arXiv2024

Critical quantum dynamics of observables at eigenstate transitions

It is an outstanding goal to unveil the key features of quantum dynamics at eigenstate transitions. Focusing on quadratic fermionic Hamiltonians that exhibit localization transitions, we identify physical observables that exhibit scale-invariant critical dynamics at the transition when quenched from the initially localized charge density-wave states. The identification is based on two ingredients: (a) A relationship between the time evolution of observables in a many-body state and the transition probabilities of single-particle states, and (b) scale invariance of transition probabilities, which generalizes the corresponding recent result for survival probabilities [M. Hopjan and L. Vidmar, Phys. Rev. Lett. 131, 060404 (2023); Phys. Rev. Res. 5, 043301 (2023)]. These properties suggest that the scale-invariant critical dynamics in the quantum-quench dynamics is also exhibited by the observables, which share the common eigenbasis with the Hamiltonian before the quench. Focusing on experimentally relevant observables such as site occupations and the particle imbalance, we numerically demonstrate their critical behavior at the eigenstate transitions in the three-dimensional Anderson model and the one-dimensional Aubry-André model model.

cond-mat.stat-mech↗

arXiv2024

Similarity between a many-body quantum avalanche model and the ultrametric random matrix model

In the field of ergodicity-breaking phases, it has been recognized that quantum avalanches can destabilize many-body localization at a wide range of disorder strengths. This has in particular been demonstrated by the numerical study of a toy model, sometimes simply called the "avalanche model" or the "quantum sun model" [Phys. Rev. Lett. 129, 060602 (2022)], which consists of an ergodic seed coupled to a perfectly localized material. In this paper, we connect this toy model to a well-studied model in random matrix theory, the ultrametric ensemble. We conjecture that the models share the following features. 1) The location of the critical point may be predicted sharply by analytics. 2) On the localized site, both models exhibit Fock space localization. 3) There is a manifold of critical points. On the critical manifold, the eigenvectors exhibit nontrivial multifractal behaviour that can be tuned by moving on the manifold. 4) The spectral statistics at criticality is intermediate between Poisson statistics and random matrix statistics, also tunable on the critical manifold. We confirm numerically these properties.

cond-mat.stat-mech↗

arXiv2023

Scale-invariant critical dynamics at eigenstate transitions

The notion of scale-invariant dynamics is well established at late times in quantum chaotic systems, as illustrated by the emergence of a ramp in the spectral form factor (SFF). Building on the results of the preceding Letter [Phys. Rev. Lett. 131, 060404 (2023)], we explore features of scale-invariant dynamics of survival probability and SFF at criticality, i.e., at eigenstate transitions from quantum chaos to localization. We show that, in contrast to the quantum chaotic regime, the quantum dynamics at criticality do not only exhibit scale invariance at late times, but also at much shorter times that we refer to as mid-time dynamics. Our results apply to both quadratic and interacting models. Specifically, we study Anderson models in dimensions three to five and power-law random banded matrices for the former, and the quantum sun model and the ultrametric model for the latter, as well as the Rosenzweig-Porter model.

cond-mat.stat-mech↗

arXiv2023

Scale-Invariant Survival Probability at Eigenstate Transitions

Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here we argue that a scaled survival probability, where time is measured in units of a typical Heisenberg time, exhibits a scale-invariant behavior at eigenstate transitions. We first demonstrate this property in two paradigmatic quadratic models, the one-dimensional Aubry-Andre model and three-dimensional Anderson model. Surprisingly, we then show that similar phenomenology emerges in the interacting avalanche model of ergodicity breaking phase transitions. This establishes an intriguing similarity between localization transition in quadratic systems and ergodicity breaking phase transition in interacting systems.

quant-ph↗

arXiv2022

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

cond-mat.mtrl-sci↗

arXiv2021

Detecting delocalization-localization transitions from full density distributions

Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is a key open question in the field of nonequilibrium physics. We exploit that localization of particles as realized in Anderson and standard many-body localization (MBL) implies Fock-space localization in single-particle basis sets characterized by a real-space index. Using a recently introduced quantitative measure for Fock-space localization computed from the density distributions, the occupation distance, we systematically study its scaling behavior across delocalozation transitions and identify critical points from scaling collapses of numerical data. Excellent agreement with literature results is found for the critical disorder strengths of noninteracting fermions, such as the one-dimensional Aubry-André and the three-dimensional Anderson model. We observe a distinctively different scaling behavior in the case of interacting fermions with random disorder consistent with a Kosterlitz-Thouless transition. Finally, we use our measure to extract the transition point as a function of filling for interacting fermions.

cond-mat.dis-nn↗

arXiv2021

Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems

We investigate a spatial subsystem entropy extracted from the one-particle density matrix (OPDM) in one-dimensional disordered interacting fermions that host a many-body localized (MBL) phase. Deep in the putative MBL regime, this OPDM entropy exhibits the salient features of localization, despite not being a proper entanglement measure. We numerically show that the OPDM entropy of the eigenstates obeys an area law. Similar to the von-Neumann entropy, the OPDM entropy grows logarithmically with time after a quantum quench, albeit with a different prefactor. Both these features survive at moderately large interactions and well towards the transition into the ergodic phase. The computational cost to calculate the OPDM entropy scales only polynomially with the system size, suggesting that the OPDM provides a promising starting point for developing diagnostic tools for MBL in simulations and experiments.

cond-mat.str-el↗

arXiv2020

Many-body localization from a one-particle perspective in the disordered 1D Bose-Hubbard model

We numerically investigate 1D Bose-Hubbard chains with onsite disorder by means of exact diagonalization. A primary focus of our work is on characterizing Fock-space localization in this model from the single-particle perspective. For this purpose, we compute the one-particle density matrix (OPDM) in many-body eigenstates. We show that the natural orbitals (the eigenstates of the OPDM) are extended in the ergodic phase and real-space localized when one enters into the MBL phase. Furthermore, the distributions of occupations of the natural orbitals can be used as measures of Fock-space localization in the respective basis. Consistent with previous studies, we observe signatures of a transition from the ergodic to the many-body localized (MBL) regime when increasing the disorder strength. We further demonstrate that Fock-space localization, albeit weaker, is also evidently present in the distribution of the physical densities in the MBL regime, both for soft- and hardcore bosons. Moreover, the full distribution of the densities of the physical particles provides a one-particle measure for the detection of the ergodic-MBL transition which could be directly accessed in experiments with ultra-cold gases.

cond-mat.str-el↗