arXiv subjects

Jan Carl Budich

Publications and source records attributed to Jan Carl Budich.

At least 19 recordsLinked to original sources

arXiv2026

Diffusion in quantum state preparation: From passive cooling to system-bath engineering

We investigate and compare two particle number-conserving protocols for the preparation of a topologically nontrivial state. The first is derived from thermally coupling the system to a cold bath, while the second is based on engineered dissipation. We numerically study the time required to reach the target state as well as its robustness against physically important perturbations. Crucially, in both protocols, the cooling capability is limited by dissipatively induced diffusion processes. The resulting quadratic scaling of the cooling time with system size is also corroborated analytically using mean-field approximations and a purely classical random-walk model. Furthermore, we find that the engineered protocol admits a unique and stable dark state, which contributes to an ongoing discussion regarding the applicability of dissipative state preparation to many-body systems.

cond-mat.quant-gas↗

arXiv2026

Liouvillian topology and nonreciprocal dynamics in open Floquet chains

Open quantum systems far from thermal equilibrium can exhibit remarkable physical phenomena including topological properties without a direct equilibrium counterpart. Along these lines, in periodically driven-dissipative systems within the effective non-Hermitian (NH) Hamiltonian approximation spectral winding numbers have been linked to intriguing nonreciprocal transport properties. Here, going beyond an NH Hamiltonian description, we introduce and study a microscopic lattice model of a driven open quantum system described by a Markovian quantum master equation, which exhibits the mentioned spectral winding within an NH approximation. By encompassing quantum jump processes in the topological analysis, we uncover a distinct \emph{jump-induced} topological phase, which qualitatively corresponds to the richer nonreciprocal transport properties of the fully quantum model. In addition, we find that the NH skin effect, i.e., the accumulation of a macroscopic number of eigenstates at one end of the system, is already visible in the transient dynamics even for systems with periodic boundary conditions. Our results exemplify the subtle correspondence between NH topological properties and physical manifestations of Liouvillian topological properties in open quantum systems, thus providing a theoretical framework towards understanding unidirectional transport in quantum dissipative Floquet dynamics.

cond-mat.mes-hall↗

arXiv2026

Entanglement Barriers from Computational Complexity: Matrix-Product-State Approach to Satisfiability

We approach the 3-SAT satisfiability problem with the quantum-inspired method of imaginary time propagation (ITP) applied to matrix product states (MPS) on a classical computer. This ansatz is fundamentally limited by a quantum entanglement barrier that emerges in imaginary time, reflecting the exponential hardness expected for this NP-complete problem. Strikingly, we argue based on careful analysis of the structure imprinted onto the MPS by the 3-SAT instances that this barrier arises from classical computational complexity. To reveal this connection, we elucidate with stochastic models the specific relationship between the classical hardness of the $\sharp$P $\supseteq$ NP-complete counting problem $\sharp$3-SAT and the entanglement properties of the quantum state. Our findings illuminate the limitations of this quantum-inspired approach and demonstrate how purely classical computational complexity can manifest in quantum entanglement. Furthermore, we present estimates of the non-stabilizerness required by the protocol, finding a similar resource barrier. Specifically, the necessary amount of non-Clifford operations scales superlinearly in system size, thus implying extensive resource requirements of ITP on different architectures such as Clifford circuits or gate-based quantum computers.

quant-ph↗

arXiv2025

Asymptotic Exceptional Steady States in Dissipative Dynamics

Spectral degeneracies in Liouvillian generators of dissipative dynamics generically occur as exceptional points, where the corresponding non-Hermitian operator becomes non-diagonalizable. Steady states, i.e. zero-modes of Liouvillians, are considered a fundamental exception to this rule since a no-go theorem excludes non-diagonalizable degeneracies there. Here, we demonstrate that the crucial issue of diverging timescales in dissipative state preparation is largely tantamount to an asymptotic approach towards the forbidden scenario of an exceptional steady state in the thermodynamic limit. With case studies ranging from NP-complete satisfiability problems encoded in a quantum master equation to the dissipative preparation of a symmetry protected topological phase, we reveal the close relation between the computational complexity of the problem at hand, and the finite size scaling towards the exceptional steady state, exemplifying both exponential and polynomial scaling. Formally treating the weight $W$ of quantum jumps in the Lindblad master equation as a parameter, we show that exceptional steady states at the physical value $W=1$ may be understood as a critical point hallmarking the onset of dynamical instability.

quant-ph↗

arXiv2025

Quantum Hall Effect without Chern Bands

The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here, further extending the realm of the quantum Hall effect, we report on the robust occurrence of an integer quantized transverse conductance at the onset of disorder in a microscopic lattice model, all bands of which are topologically trivial (zero Chern number). We attribute this phenomenon to the energetic separation of nonquantized Berry fluxes within those bands. Adding disorder then nudges the system into a quantum Hall phase from an extended critical regime obtained by placing the Fermi energy within a broad window inside a trivial band. This natural integer-rounding mechanism manifests as the mobility-gap-induced quantization of a nonuniversal Hall conductance. Our results are corroborated by numerical transport simulations and the analysis of two complementary topological markers.

cond-mat.mes-hall↗

arXiv2025

Probing Green's Function Zeros by Co-tunneling through Mott Insulators

Quantum tunneling experiments have provided deep insights into basic excitations occurring as Green's function poles in the realm of complex quantum matter. However, strongly correlated quantum materials also allow for Green's functions zeros (GFZ) that may be seen as an antidote to the familiar poles, and have so far largely eluded direct experimental study. Here, we propose and investigate theoretically how co-tunneling through Mott insulators enables direct access to the shadow band structure of GFZ. In particular, we derive an effective Hamiltonian for the GFZ that is shown to govern the co-tunneling amplitude and reveal fingerprints of many-body correlations clearly distinguishing the GFZ structure from the underlying free Bloch band structure of the system. Our perturbative analytical results are corroborated by numerical data both in the framework of exact diagonalization and matrix product state simulations for a one-dimensional model system consisting of a Su-Schrieffer-Heeger-Hubbard model coupled to two single level quantum dots.

cond-mat.str-el↗

arXiv2025

Adiabatic preparation of a number-conserving atomic Majorana phase

We construct a protocol to adiabatically prepare the ground state of a widely discussed number-conserving model Hamiltonian for ultracold atoms in optical lattices that supports Majorana edge states. In particular, we introduce a symmetry breaking mass term that amounts to threading a commensurate (artificial) magnetic flux through the plaquettes of the considered two-leg ladder which opens a constant bulk gap. This enables the preparation of the topological Majorana phase from a trivial Mott insulator state with optimal asymptotic scaling of the ramp time in system size, which is linear owing to the critical nature of the target state. Using constructive bosonization techniques that account for both finite size effects and global fermion number conservation, we are able to fully explain with theory the somewhat counterintuitive necessity of the aforementioned commensurate flux for a controlled bulk gap. Our analytical predictions are corroborated and quantified by unbiased numerical matrix product states (MPS) simulations. Directly building up on previous experimental work, the crucial flux-term of the proposed protocol is feasible with state-of-the-art experimental techniques in atomic quantum simulators.

cond-mat.quant-gas↗

arXiv2024

Dissipative frequency converter: from Lindblad dynamics to non-Hermitian topology

A topological frequency converter represents a dynamical counterpart of the integer quantum Hall effect, where a two-level system enacts a quantized time-averaged power transfer between two driving modes of incommensurate frequency. Here, we investigate as to what extent temporal coherence in the quantum dynamics of the two-level system is important for the topological quantization of the converter. To this end, we consider dissipative channels corresponding to spontaneous decay and dephasing in the instantaneous eigenbasis of the Hamiltonian as well as spontaneous decay in a fixed basis. The dissipation is modelled using both a full Lindblad and an effective non-Hermitian (NH) Hamiltonian description. For all three dissipation channels we find a transition from the unperturbed dynamics to a quantum watchdog effect, which destroys any power transfer in the strong coupling limit. This is striking because the watchdog effect leads to perfectly adiabatic dynamics in the instantaneous eigenbasis, at first glance similar to the unperturbed case. Furthermore, it is found that dephasing immediately leads to an exponential decay of the power transfer in time due to loss of polarisation in the mixed quantum state. Finally, we discuss the appearance in the effective NH trajectory description of non-adiabatic processes, which are suppressed in the full Lindblad dynamics.

cond-mat.mes-hall↗

arXiv2024

Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States

Entanglement properties of purified quantum states are of key interest for two reasons. First, in quantum information theory, minimally entangled purified states define the Entanglement of Purification as a fundamental measure for the complexity of the corresponding physical mixed state. Second, dynamical entanglement growth in purified states represents the main bottleneck for calculating dynamical physical properties on classical computers in the framework of tensor network states. Here, we demonstrate how geometric methods including parallel transport may be harnessed to reduce such dynamical entanglement growth, and to obtain a general prescription for maintaining (locally) optimal entanglement entropy when time-evolving a purified state. Adapting and extending by higher order skew corrections the notion of Uhlmann geometric phases, we reveal the relation between dynamical entanglement growth and the geometry of the Hilbert-Schmidt bundle as the mathematical foundation of purified states. With benchmarks on a non-integrable spin chain model, we compare the computational performance of matrix product state algorithms based on our present geometric disentangling method to previous approaches for taming entanglement growth in purified states. Our findings provide numerical evidence that geometric disentanglers are a powerful approach, superior in various aspects to known methods for disentangling purified states in a range of physically relevant computational scenarios. To exclude the effect of algorithmic imperfections, we also provide a numerically exact analysis for systems of moderate size.

cond-mat.str-el↗

arXiv2024

Nodal Spectral Functions Stabilized by Non-Hermitian Topology of Quasiparticles

In quantum materials, basic observables such as spectral functions and susceptibilities are determined by Green's functions and their complex quasiparticle spectrum rather than by bare electrons. Even in closed many-body systems, this makes a description in terms of effective non-Hermitian (NH) Bloch Hamiltonians natural and intuitive. Here, we discuss how the abundance and stability of nodal phases is drastically affected by NH topology. While previous work has mostly considered complex degeneracies known as exceptional points as the NH counterpart of nodal points, we propose to relax this assumption by only requiring a crossing of the real part of the complex quasiparticle spectra, which entails a band crossing in the spectral function, i.e. a nodal spectral function. Interestingly, such real crossings are topologically protected by the braiding properties of the complex Bloch bands, and thus generically occur already in one-dimensional systems without symmetry or fine-tuning. We propose and study a microscopic lattice model in which a sublattice-dependent interaction stabilizes nodal spectral functions. Besides the gapless spectrum, we identify non-reciprocal charge transport properties after a local potential quench as a key signature of non-trivial band braiding. Finally, in the limit of zero interaction on one of the sublattices, we find a perfectly ballistic unidirectional mode in a non-integrable environment, reminiscent of a chiral edge state known from quantum Hall phases. Our analysis is corroborated by numerical simulations both in the framework of exact diagonalization and within the conserving second Born approximation.

cond-mat.mes-hall↗

arXiv2024

Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities

At thermal equilibrium, we find that generalized susceptibilities encoding the static physical response properties of Hermitian many-electron systems possess inherent non-Hermitian (NH) matrix symmetries. This leads to the generic occurrence of exceptional points (EPs), i.e., NH spectral degeneracies, in the generalized susceptibilities of prototypical Fermi-Hubbard models, as a function of a single parameter such as chemical potential. We demonstrate that these EPs are necessary to promote correlation-induced thermodynamic instabilities, such as phase-separation occurring in the proximity of a Mott transition, to a topologically stable phenomenon.

cond-mat.str-el↗

arXiv2024

Long time rigidity to flux-induced symmetry breaking in quantum quench dynamics

We investigate how the breaking of charge conjugation symmetry $\mathcal{C}$ impacts on the dynamics of a half-filled fermionic lattice system after global quenches. We show that, when the initial state is insulating and the $\mathcal{C}$-symmetry is broken non-locally by a constant magnetic flux, local observables and correlations behave as if the symmetry were unbroken for a time interval proportional to the system size $L$. In particular, the local particle density of a quenched dimerized insulator remains pinned to $1/2$ in each lattice site for an extensively long time, while it starts to significantly fluctuate only afterwards. Due to its qualitative resemblance to the sudden arrival of rapidly rising ocean waves, we dub this phenomenon the ``tsunami effect". Notably, it occurs even though the chiral symmetry is dynamically broken right after the quench. Furthermore, we identify a way to quantify the amount of symmetry breaking in the quantum state, showing that in insulators perturbed by a flux it is exponentially suppressed as a function of the system size, while it is only algebraically suppressed in metals and in insulators with locally broken $\mathcal{C}$-symmetry. The robustness of the tsunami effect to weak disorder and interactions is demonstrated, and possible experimental realizations are proposed.

cond-mat.quant-gas↗

arXiv2023

Correlation-Induced Sensitivity and Non-Hermitian Skin Effect of Quasiparticles

Non-Hermitian (NH) Hamiltonians have been shown to exhibit unique signatures, including the NH skin effect and an exponential spectral sensitivity with respect to boundary conditions. Here, we investigate as to what extent these remarkable phenomena, recently predicted and observed in a broad range of settings, may also occur in closed correlated fermionic systems that are governed by a Hermitian many-body Hamiltonian. There, an effectively NH quasiparticle description naturally arises in the Green's function formalism due to inter-particle scattering that represents an inherent source of dissipation. As a concrete platform we construct an extended interacting Su-Schrieffer-Heeger (SSH) model subject to varying boundary conditions, which we analyze using exact diagonalization and non-equilibrium Green's function methods. That way, we clearly identify the presence of the aforementioned NH phenomena in the quasi-particle properties of this Hermitian model system.

cond-mat.mes-hall↗

arXiv2023

Braid Protected Topological Band Structures with Unpaired Exceptional Points

We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e. the necessity of compensating the topological charge of a stable nodal point by an anti-dote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how noncommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions.

cond-mat.mes-hall↗

arXiv2023

Spontaneous Formation of Exceptional Points at the Onset of Magnetism

We reveal how symmetry protected nodal points in topological semimetals may be promoted to pairs of generically stable exceptional points (EPs) by symmetry-breaking fluctuations at the onset of long-range order. This novel route to non-Hermitian (NH) topology is exemplified by a magnetic NH Weyl phase spontaneously emerging at the surface of a strongly correlated three-dimensional topological insulator when entering the ferromagnetic regime from a high temperature paramagnetic phase. Here, electronic excitations with opposite spin acquire significantly different life-times, thus giving rise to an anti-Hermitian structure in spin that is incompatible with the chiral spin texture of the nodal surface states, and hence facilitates the spontaneous formation of EPs. We present numerical evidence of this phenomenon by solving a microscopic multi-band Hubbard model non-perturbatively in the framework of dynamical mean-field theory.

cond-mat.str-el↗

arXiv2023

Non-Linear Interference Challenging Topological Protection of Chiral Edge States

We report on a non-linear scattering effect that challenges the notion of topological protection for wave packets propagating in chiral edge modes. Specifically, in a Floquet topological system close to resonant driving and with a non-linear potential, we demonstrate how a wave packet propagating in a chiral edge mode may be irreversibly deflected by scattering off a localized wave-packet, or pass the collision region virtually unaffected in an approximately linear fashion. An experimentally accessible knob to tune between those two scenarios is provided by the relative phase between the involved wave-packets. This genuinely non-linear interference phenomenon is in stark contrast to linear scattering off a static impurity, which cannot destroy a topological edge state. Besides corroborating our findings with numerically exact simulations, we propose two physical platforms where our predictions may be verified with state of the art experimental techniques: First, a coupled waveguide setting where non-linearity has been engineered via an intensity-dependent optical index. Second, a Bose-Einstein condensate of cold atoms in an optical Honeycomb lattice governed by a non-linear Gross-Pitaevskii equation that effectively accounts for many-body interactions.

cond-mat.quant-gas↗

arXiv2023

Non-Hermitian topological ohmmeter

Measuring large electrical resistances forms an essential part of common applications such as insulation testing, but suffers from a fundamental problem: the larger the resistance, the less sensitive a canonical ohmmeter is. Here we develop a conceptually different electronic sensor by exploiting the topological properties of non-Hermitian matrices, whose eigenvalues can show an exponential sensitivity to perturbations. The ohmmeter is realized in an multi-terminal, linear electric circuit with a non-Hermitian conductance matrix, where the target resistance plays the role of the perturbation. We inject multiple currents and measure a single voltage in order to directly obtain the value of the resistance. The relative accuracy of the device increases exponentially with the number of terminals, and for large resistances outperforms a standard measurement by over an order of magnitude. Our work paves the way towards leveraging non-Hermitian conductance matrices in high-precision sensing.

cond-mat.mes-hall↗

arXiv2023

Topology in the space-time scaling limit of quantum dynamics

We investigate the role of topology in the space-time scaling limit of quantum quench dynamics, where both time and system size tend to infinity at a constant ratio. There, while the standard topological characterization relying on local unitary transformations becomes ill defined, we show how a different dynamical notion of topology naturally arises through a dynamical winding number encoding the linear response of the Berry phase to a magnetic flux. Specifically, we find that the presence of a locally invisible constant magnetic flux is revealed by a dynamical staircase behavior of the Berry phase, whose topologically quantized plateaus characterize the space-time scaling limit of a quenched Rice-Mele model. These jumps in the Berry phase are also shown to be related to the interband elements of the DC current operator. We outline possible experimental platforms for observing the predicted phenomena in finite systems.

cond-mat.quant-gas↗