arXiv subjects

J. Sirker

Publications and source records attributed to J. Sirker.

At least 19 recordsLinked to original sources

arXiv2026

Parastatistics in Interacting Periodic Chains Revealed by Peierls Phase Twists and Shifted Conformal Towers

We consider interacting paraparticle chains with a constant $R$-matrix where the Hamiltonian sums over the internal degrees (flavors) of the paraparticles. For such flavor-blind Hamiltonians we show a general factorization of the Hilbert space into occupation and flavor parts with the Hamiltonian acting non-trivially only on the former. For open boundaries, the spectrum therefore coincides with that of the occupation Hamiltonian $H_{\rm occ}$ with the flavor part merely adding degeneracies. For periodic boundaries, a cyclic reordering of the flavors leads to a separation of $H_{\rm occ}$ into flux sectors at fixed particle number, thus making the parastatistics directly observable in the energy spectrum. For important exemplary cases, $H_{\rm occ}$ reduces to the XXZ chain with flux allowing for an exact solution. In the gapless regime, this solution shows flux-shifted $c=1$ conformal towers in the low-energy spectrum and a temperature-dependent chemical potential in the bulk thermodynamics.

cond-mat.stat-mech↗

arXiv2026

Length-resolved Operator Growth and Path-Entropy Obstructions to Many-Body Localization

For the disordered Ising chain with transverse and longitudinal fields, where couplings and fields are drawn from strictly positive distributions, Cao~\cite{Cao} has shown that the moments $μ_{2k} = \|[H,σ^z_0]^{(k)}\|_2^2$ grow almost factorially, $μ_{2k}^{1/(2k)}\sim k/\ln k$, and thus asymptotically at the maximal allowed rate. We generalize this result by resolving the operator norm in support length and show that the weight at length $\ell_k \sim k/\ln k$ already exhibits almost factorial growth, $\|[H,σ^z_0]^{(k)}_{\ell_k}\|_2 \gtrsim (k/\ln k)^k$. This implies maximal spatial delocalization of local operators and, in particular, rules out dynamical locality---the strongest form of many-body localization---at any disorder strength. We further establish rigorously a finite-size crossover scale $L\sim (W/J)^2$, where $W$ is the disorder and $J$ the coupling strength. For $L\lesssim (W/J)^2$ numerical studies only access a pre-asymptotic regime. Finally, we identify a structural path-entropy obstruction to perturbative LIOM constructions, based on the almost factorial branching of operator content and independent of resonance effects; the same mechanism strongly suggests ballistic real-time operator spreading, so sub-ballistic or localized dynamics would require a presently unidentified cancellation principle acting on almost factorially many disorder-dependent paths with random amplitudes.

cond-mat.dis-nn↗

arXiv2026

Pseudospectral phenomena and the origin of the non-Hermitian skin effect

The non-Hermitian skin effect (NHSE), characterized by a macroscopic accumulation of eigenstates at the edge of a system with open boundaries, is often ascribed to a non-trivial point-gap topology of the Bloch Hamiltonian. We revisit this connection and separate the question of the NHSE as a spectral reconstruction effect in clean systems from the question of stable topological protection. For a Hatano-Nelson ladder, where point-gap winding and non-normality can be varied independently, we demonstrate that, in a clean translationally invariant multiband setting, the NHSE can occur without point-gap winding and, conversely, that point-gap winding can persist without the NHSE. These results establish that in the clean case the connection between point-gap winding and the NHSE only holds in the scalar one-band case but, in general, not in the multiband case. Even more importantly, the eigenspectrum of non-normal operators is generically highly sensitive to boundary conditions and perturbations, and therefore does not constitute a stable object encoding topological information. Instead, topological properties are reflected in the splitting of the singular-value spectrum for finite systems and, in the semi-infinite limit, correspond to boundary-localized kernel modes implied by the index of the corresponding Toeplitz operator.

cond-mat.stat-mech↗

arXiv2026

Comment on: "Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions"

In Ref. [1], dynamical quantum phase transitions (DQPTs) -- non-analyticities in the Loschmidt return rate at critical times -- are investigated in the presence of noise for a two-band model. The authors report that DQPTs persist even after averaging over the noise and they use their results to derive dynamical phase diagrams. The protocol used approximates the noise-averaged mixed state, obtained using a master equation, by a pure state, characterized by its excitation probability. In this comment we rigorously show that: (1) This approximation is exponentially poor in the thermodynamic limit. (2) When using the correct metric, the Loschmidt echo of two density matrices in any two-dimensional Hilbert space can become zero if and only if {\it both} density matrices are pure, ruling out DQPTs for non-zero noise. (3) An a posteriori reinterpretation of the results as an interferometric protocol is possible but such a protocol is unsuitable to investigate the effects of noise on DQPTs because it is inherently blind to decoherence. We also investigate alternative natural ways to average over noise realizations and show that in all of them DQPTs are smoothed out.

cond-mat.stat-mech↗

arXiv2026

Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values

In contrast to eigenvalue-based approaches, we formulate the bulk-boundary correspondence for two-dimensional non-Hermitian quadratic lattice Hamiltonians in terms of Toeplitz operators and singular values, which correctly capture the stability, localization, and scaling of edge and corner modes. We show that singular values, rather than eigenvalues, provide the only stable foundation for topological protection in non-Hermitian systems because they remain robust under translational-symmetry-breaking perturbations that destabilize the eigenvalue spectrum, rendering it unsuitable for topological classification. Building on Toeplitz operator theory, we establish general results for non-Hermitian Hamiltonians defined on half and quarter planes, relating the topological indices of the associated Toeplitz operators to the number of finite-size singular values that are separated from the bulk singular-value spectrum and vanish in the thermodynamic limit. This yields a precise bulk-boundary correspondence for edge and corner modes, including higher-order topological phases, without requiring crystalline symmetries. We illustrate our general results with detailed examples exhibiting topologically protected families of edge states, coexisting edge and corner modes, and phases with both gapped bulk and edges supporting only stable corner modes. The latter is exemplified by a non-Hermitian generalization of the Benalcazar-Bernevig-Hughes model.

cond-mat.stat-mech↗

arXiv2025

Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization

We consider the spreading of a local operator $A$ in one-dimensional systems with Hamiltonian $H$ by calculating the $k$-fold commutator $[H,[H,[...,[H,A]]]]$. We derive bounds for the operator norm of this commutator in free and interacting systems with and without disorder thus directly connecting the operator growth hypothesis with questions of localization. We analytically show that an almost factorial growth of the operator norm - as recently proven for the random Ising model - is inconsistent with an exponential localization of $A$. Assuming that a quasi-local unitary $U$ exists which maps $H$ onto an effective Hamiltonian $\tilde H=UHU^\dagger=\sum_n E_n τ^z_n +\sum_{i,j} J_{ij} τ^z_iτ^z_j+\dots$, we show that $\tilde A=UAU^\dagger$ is a quasi-local operator which in the many-body case does not remain exponentially localized in general leading to an almost factorial norm growth. Therefore the unitary $U$ in many-body systems with maximal norm growth either does not exist and such systems are always ergodic or unusual non-ergodic phases described by $\tilde H$ do exist which violate the operator growth hypothesis and in which operators spread, implying that transport will eventually set in. We analytically and symbolically verify our results for the Anderson and Aubry-André models. For the XXX case, the symbolic calculations are consistent with a maximal norm growth. Furthermore, we find no indication of a weakened exponential localization of $A$, expected for strong disorder and low commutator orders if the unitary $U$ does exist. Finally, we try to perturbatively construct $U$ by consecutive Schrieffer-Wolff transformations. While it is straightforward to show that this construction converges in the Anderson case, we find no indications for a convergence in the interacting case, suggesting that $U$ does not exist and that many-body localization is absent.

cond-mat.dis-nn↗

arXiv2025

Hidden zero modes and topology of multiband non-Hermitian systems

In a finite one-dimensional non-Hermitian system, the number of zero modes does not necessarily reflect the topology of the system. This is known as the breakdown of the bulk-boundary correspondence and has led to misconceptions about the topological protection of edge modes in such systems. Here we show why this breakdown does occur and that it typically results in hidden zero modes, extremely long-lived zero energy excitations, which are only revealed when considering the singular value instead of the eigenvalue spectrum. We point out, furthermore, that in a finite multiband non-Hermitian system with Hamiltonian $H$, one needs to consider also the reflected Hamiltonian $\tilde H$, which is in general distinct from the adjoint $H^\dagger$, to properly relate the number of protected zeroes to the winding number of $H$.

cond-mat.stat-mech↗

arXiv2024

Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction

We investigate how topological Chern numbers can be defined when single-particle states hybridize with continua. We do so exemplarily in a bosonic Haldane model at zero temperature with an additional on-site decay of one boson into two and the conjugate fusion of two bosons into one. Restricting the Hilbert space to two bosons at maximum, the exact self-energy is accessible. We use the bilinear Hamiltonian $H_0$ corrected by the self-energy $Σ$ to compute Chern numbers by two different approaches. The results are gauged against a full many-body calculation in the Hilbert space where possible. We establish numerically and analytically that the effective Hamiltonian $H_\text{eff}=H_0(\vec k) +Σ(ω,\vec k)$ reproduces the correct many-body topology if the considered band does not overlap with the continuum. In case of overlaps, one can extend the definition of the Chern number to the non-Hermitian $H_\text{eff}$ and there is evidence that the Chern number changes at exceptional points. But the bulk-boundary correspondence appears to be no longer valid and edge modes delocalize.

cond-mat.mes-hall↗

arXiv2024

Thermodynamics based on Neural Networks

We present three different neural network algorithms to calculate thermodynamic properties as well as dynamic correlation functions at finite temperatures for quantum lattice models. The first method is based on purification, which allows for the exact calculation of the operator trace. The second one is based on a sampling of the trace using minimally entangled states, whereas the third one makes use of quantum typicality. In the latter case, we approximate a typical infinite-temperature state by wave functions which are given by a product of a projected pair and a neural network part and evolve this typical state in imaginary time.

cond-mat.stat-mech↗

arXiv2023

Entanglement and particle fluctuations of one-dimensional chiral topological insulators

We consider the topological protection of entanglement and particle fluctuations for a general one-dimensional chiral topological insulator with winding number $\mathcal{I}$. We prove, in particular, that when the periodic system is divided spatially into two equal halves, the single-particle entanglement spectrum has $2|\mathcal{I}|$ protected eigenvalues at $1/2$. Therefore the number fluctuations are bounded from below by $ΔN^2\geq |\mathcal{I}|/2$ and the entanglement entropy by $S\geq 2|\mathcal{I}|\ln 2$. We note that our results are obtained by applying directly an index theorem to the microscopic model and do not rely on an equivalence to a continuum model or a bulk-boundary correspondence for a slow varying boundary.

cond-mat.str-el↗

arXiv2023

Symmetry-Resolved Entanglement: General considerations, calculation from correlation functions, and bounds for symmetry-protected topological phases

We discuss some general properties of the symmetry-resolved von-Neumann entanglement entropy in systems with particle number conservation and describe how to obtain the entanglement components from correlation functions for Gaussian systems. We introduce majorization as an important tool to derive entanglement bounds. As an application, we derive lower bounds both for the number and the configurational entropy for chiral and Cn-symmetric topological phases. In some cases, our considerations also lead to an improvement of the previously known lower bounds for the entanglement entropy in such systems.

cond-mat.stat-mech↗

arXiv2022

Symmetry-Resolved Entanglement of $C_2$-symmetric Topological Insulators

For a many-body system of arbitrary dimension, we consider fermionic ground states of non-interacting Hamiltonians invariant under a $C_2$ cyclic group. The absolute difference $Δ$ between the number of occupied symmetric and anti-symmetric single-particle states is an adiabatic invariant. We prove lower bounds on the configurational and the number entropy based on this invariant. In band insulators, the topological invariant $Δ$ and the entropy bounds can be directly determined from high symmetry points in the Brillouin zone.

cond-mat.str-el↗

arXiv2022

Non-linear Transport by Bethe Bound States

We consider non-linear ballistic spin transport in the XXZ spin chain and derive an analytical result for the non-linear Drude weight $D^{(3)}$ at infinite temperatures. In contrast to the linear Drude weight $D^{(1)}$, we find that the result not only depends on anisotropy but also on the string length of the quasiparticles transporting the spin current. Our result provides further insights into transport by quasiparticles and raises questions about Luttinger liquid universality.

cond-mat.str-el↗

arXiv2020

Unlimited growth of particle fluctuations in many-body localized phases

We study quench dynamics in a t-V chain of spinless fermions (equivalent to the spin-1/2 Heisenberg chain) with strong potential disorder. For this prototypical model of many-body localization we have recently argued that -- contrary to the established picture -- particles do not become fully localized. Here we summarize and expand on our previous results for various entanglement measures such as the number and the Hartley number entropy. We investigate, in particular, possible alternative interpretations of our numerical data. We find that none of these alternative interpretations appears to hold and, in the process, discover further strong evidence for the absence of localization. Furthermore, we obtain more insights into the entanglement dynamics and the particle fluctuations by comparing with non-interacting systems where we derive several strict bounds. We find that renormalized versions of these bounds also hold in the interacting case where they provide support for numerically discovered scaling relations between number and entanglement entropies.

cond-mat.dis-nn↗

arXiv2020

Operational Entanglement of Symmetry-Protected Topological Edge States

We use an entanglement measure that respects the superselection of particle number to study the non-local properties of symmetry-protected topological edge states. Considering half-filled M-leg Su-Schrieffer-Heeger (SSH) ladders as an example, we show that the topological properties and the operational entanglement extractable from the boundaries are intimately connected. Topological phases with at least two filled edge states have the potential to realize genuine, non-bipartite, many-body entanglement which can be transferred to a quantum register. The entanglement is extractable when the filled edge states are sufficiently localized on the lattice sites controlled by the users. We show, furthermore, that the onset of entanglement between the edges can be inferred from local particle number spectroscopy alone and present an experimental protocol to study the breaking of Bell's inequality.

quant-ph↗

arXiv2020

Entanglement dynamics in the three-dimensional Anderson model

We numerically study the entanglement dynamics of free fermions on a cubic lattice with potential disorder following a quantum quench. We focus, in particular, on the metal-insulator transition at a critical disorder strength and compare the results to the putative many-body localization (MBL) transition in interacting one-dimensional systems. We find that at the transition point the entanglement entropy grows logarithmically with time $t$ while the number entropy grows $\sim\ln\ln t$. This is exactly the same scaling recently found in the MBL phase of the Heisenberg chain with random magnetic fields suggesting that the MBL phase might be more akin to an extended critical regime with both localized and delocalized states rather than a fully localized phase. We also show that the experimentally easily accessible number entropy can be used to bound the full entanglement entropy of the Anderson model and that the critical properties at the metal-insulator transition obtained from entanglement measures are consistent with those obtained by other probes.

cond-mat.dis-nn↗

arXiv2019

Transport in one-dimensional integrable quantum systems

These notes are based on a series of three lectures given at the Les Houches summer school on 'Integrability in Atomic and Condensed Matter Physics' in August 2018. They provide an introduction into the unusual transport properties of integrable models in the linear response regime focussing, in particular, on the spin-1/2 XXZ spin chain.

cond-mat.str-el↗

arXiv2019

Logarithmic entanglement growth in two-dimensional disordered fermionic systems

We investigate the growth of the entanglement entropy $S_{\textrm{ent}}$ following global quenches in two-dimensional free fermion models with potential and bond disorder. For the potential disorder case we show that an intermediate weak localization regime exists in which $S_{\textrm{ent}}(t)$ grows logarithmically in time $t$ before Anderson localization sets in. For the case of binary bond disorder near the percolation transition we find additive logarithmic corrections to area and volume laws as well as a scaling at long times which is consistent with an infinite randomness fixed point.

cond-mat.dis-nn↗