arXiv subjects

Sebastian Paeckel

Publications and source records attributed to Sebastian Paeckel.

At least 19 recordsLinked to original sources

arXiv2026

Ensembles of random quantum states tunable from volume law to area law

A standard approach to generate random pure quantum states relies on sampling from the Haar measure. However, the entanglement properties of such states present a fundamental challenge for their general applicability. Here, we introduce the $\sigma$-ensembles $\unicode{x2013}$ a family of random quantum states with only a single control parameter. Crucially, these states are designed such that they can be tuned between volume-law and area-law behavior, which has been a major obstacle thus far. We construct representatives of this ensemble by imposing a probability distribution on the eigenvalues of the successive subsystems, and subsequently reconstructing a compatible global state using the matrix product state (MPS) formalism. Due to their area-law entanglement, our approach circumvents the intractability of Haar-random pure states in classical simulations of quantum systems and is more representative of typical Hamiltonian ground states.

quant-ph↗

arXiv2026

Two-channel physics in a lightly doped antiferromagnetic Mott insulator revealed by two-hole spectroscopy

Understanding pairing in the strong-coupling regime of doped Mott insulators remains an open problem in the context of cuprate superconductors. We perform ultra-high resolution numerical simulations of spectral functions in the highly underdoped $t-J$ model and discover two coupled branches of hole pairs emerging at low energies in the largely unexplored two-particle spectrum. As spin anisotropy is tuned from the Ising limit to the $SU(2)$-symmetric Heisenberg regime, the lowest $d$-wave pair evolves from a single bipolaronic branch into two hybridized branches separated by an avoided crossing. We explain this behaviour using an effective two-channel model involving a tightly bound bipolaronic state and a second channel associated with two magnetic polarons. The model reproduces the qualitative low-energy spectra and implies near-resonant $d$-wave interactions in the $SU(2)$-symmetric $t-J$ model, consistent with proximity to an emergent Feshbach-type resonance. To probe these predictions experimentally, we propose a Raman spectroscopy scheme for the attractive Hubbard model that can be directly implemented using ultracold atoms in optical lattices. Our work establishes two-particle spectroscopy, beyond single-particle Green's functions, as a powerful tool for revealing the microscopic origins of unconventional superconductivity.

cond-mat.str-el↗

arXiv2026

Adaptive Pseudoboson Density-Matrix Renormalization Group for Dilute 2D Systems

Simulating strongly correlated systems in two dimensions is notoriously challenging due to rapid entanglement growth and frustration. Here, we introduce the adaptive projected-purified pseudoboson density-matrix renormalization group (A3P-DMRG) tailored to explore the ground states of dilute lattice models. The method compresses cluster Hilbert spaces by retaining only the most probable low-occupation Fock states, identified via probabilistic bounds and refined through a self-consistent mean-field basis optimization. We demonstrate that A3P-DMRG is advantageous in low-filling and weak-coupling regimes for large system sizes where conventional DMRG struggles. This establishes the method as a versatile tool for studying dilute quantum many-body systems relevant to ultra-cold atom quantum simulators, photonic lattices, Moir\'e materials and quantum chemistry.

cond-mat.str-el↗

arXiv2025

Large Isolated Stripes on Short 18-leg $t$-$J$ Cylinders

Spin-charge stripes belong to the most prominent low-temperature orders besides superconductivity in high-temperature superconductors. This phase is particularly challenging to study numerically due to finite-size effects. By investigating the formation of long, isolated stripes, we offer a perspective complementary to typical finite-doping phase diagrams. We use the density-matrix renormalization group algorithm to extract the ground states of an 18-leg cylindrical strip geometry, making the diameter significantly wider than in previous works. This approach allows us to map out the range of possible stripe filling fractions on the electron versus hole-doped side. We find good agreement with established results, suggesting that the spread of filling fractions observed in the literature is governed by the physics of a single stripe. Taking a microscopic look at stripe formation, we reveal two separate regimes - a high-filling regime captured by a simplified squeezed-space model and a low-filling regime characterized by the structure of individual pairs of dopants. Thereby, we trace back the phenomenology of the striped phase to its microscopic constituents and highlight the different challenges for observing the two regimes in quantum simulation experiments.

cond-mat.str-el↗

arXiv2025

From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model

The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall (FQH) states and their lattice analogs - fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations and, for spinful systems, are often accompanied by ferromagnetism and skyrmions. Here, we study a Hofstadter-Hubbard model of spinful fermions on a square lattice, extended by nearest-neighbor interactions. Using large-scale density matrix renormalization group (DMRG) simulations, we demonstrate the emergence of a spin-polarized $\frac{1}{3}$-Laughlin-like FCI phase, characterized by a quantized many-body Chern number, a finite charge gap, and hidden off-diagonal long-range order. We further investigate the quantum Hall ferromagnet at $\nu=1$ and its skyrmionic excitations upon doping. In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around $\nu=1$, whereas we do not find such textures around $\nu=\frac{1}{3}$. The diagnostic toolbox presented in this work, based on local densities, correlation functions, and spin-resolved observables, is directly applicable in quantum gas microscopy experiments. Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.

cond-mat.quant-gas↗

arXiv2025

A Tensor Network Framework for Lindbladian Spectra and Steady States

Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional non-equilibrium phases beyond the Mermin-Wagner limit or dissipative state preparation demand a systematic analysis of quantum many-body phases out of equilibrium. Akin to the equilibrium case, this requires the computation of the low-lying eigenstates of Lindbladians, a problem challenging conventional approaches for simulating quantum many-body systems. Here, we undertake a first step to overcome this limitation and introduce a tensor-network-based framework to systematically compute not only steady states, but also low-lying excited states for large, driven quantum many-body systems. Our framework is based on recent advances utilizing complex-time Krylov spaces, and we leverage these ideas to create a toolbox tailored to solve the challenging non-Hermitian eigenvalue problem ubiquitous in open quantum systems. At the example of the interacting Bose-Hubbard model driven by dissipation-assisted hopping, we demonstrate the high efficiency and accuracy. From a reliable finite-size scaling analysis of the spectral gap, we find strong evidence for nonlinear hydrodynamic behavior consistent with Kardar-Parisi-Zhang-type superdiffusive relaxation and establish the existence of exponentially accelerated, anomalous relaxation. This method unlocks the capability of spectral analysis of generic open quantum many-body systems, suitable also for non-Markovian environments.

quant-ph↗

arXiv2025

Ultrafast electronic coherence from slow phonons

Light offers a route to engineer new phases of matter far from equilibrium, including transient states suggestive of superconducting, charge-ordered, and excitonic ordering behavior. Yet it remains unclear how optical excitation can dynamically produce long-range phase coherence-a defining feature of true order such as superconductivity-rather than merely enhancing local pairing. Here we show that impulsively driven low-frequency phonons enhance long-range electronic correlations in a low-dimensional metal. Through numerically exact simulations, we demonstrate that slow phonons suppress dynamical disorder, enabling buildup of coherence and enhancement of charge (and pairing) orders. These findings provide direct evidence that light can mediate enhancement of long-range order and suggest that future experimental strategies-such as the design of selective excitations of narrow phonon distributions to limit dephasing-may offer viable routes to design and stabilize transient superconducting states.

cond-mat.supr-con↗

arXiv2025

Towards effective models for low-dimensional cuprates: From ground state Hamiltonian reconstruction to spectral functions

Understanding which minimal effective model captures the essential physics of cuprates is a key step towards unraveling the mechanism behind high-$T_c$ superconductivity. Recent measurements of the dynamical spin structure factor (DSF) in cuprate ladder compounds have indicated the presence of a large effective attraction in the single-band Hubbard model, possibly mediated by phonons. Here, we demonstrate that similar DSF features can also be captured by $t$-$J$ descriptions with or even without any attractive term. Motivated by this observation, we systematically investigate the strength and origin of different contributions to the single-band Hamiltonians by downfolding either from the three-band Emery model or the electron-phonon coupled Hubbard-Holstein model. For one-dimensional systems, we find that the extended versions of both single-band descriptions can reproduce the experimentally observed DSF signatures. Finally, we extend our analysis to two dimensions by comparing two-hole correlation functions for the different single-band models. Our results provide new insights into the long-standing question of which single-band Hamiltonian can capture the essential physics of cuprates.

cond-mat.str-el↗

arXiv2025

Probing the Physical Reality of Projective Measurements

We propose a protocol to test whether the postulate of a measurement acting as an instantaneous projection onto an eigenstate of the measurement apparatus is compatible with physical reality. This approach is solely based on repeated measurements of local quantities with frequencies that are within reach of analog quantum simulation platforms, for instance Rydberg atom arrays or ultracold gases in optical lattices. Crucially, we also develop a continuous description of a quantum measurement finding that its repeated-measurement statistics (RMS) drastically differ from the projective case. This description is based on very general assumptions about quantum systems, most importantly maintaining continuous dynamics of the coherent part of the state. Our findings imply that the significantly different measurement statistics in the collapse-free description should be qualitatively replicated by any modification of standard quantum theory that is lacking explicit wave-function collapses.

quant-ph↗

arXiv2025

Fast and direct preparation of a genuine lattice BEC via the quantum Mpemba effect

We demonstrate that dissipative state preparation protocols in many-body systems can be substantially accelerated via the quantum Mpemba effect. Our approach exploits weak symmetries to analytically identify a class of simple, experimentally-realizable states that converge exponentially faster to the steady state than typical random initializations. In particular, we study the preparation of a lattice Bose-Einstein condensate (BEC), where the depletion can be controlled via the dissipation strength. We also show how to tune the momentum of the created high-fidelity BEC by combining superfluid immersion with lattice shaking. Our theoretical predictions are confirmed by numerical simulations of the dissipative dynamics. This protocol paves the way to unlock the enormous potential of the dissipative preparation of highly entangled states in analog quantum simulators.

cond-mat.quant-gas↗

arXiv2024

Spectral decomposition and high-accuracy Greens functions: Overcoming the Nyquist-Shannon limit via complex-time Krylov expansion

The accurate computation of low-energy spectra of strongly correlated quantum many-body systems, typically accessed via Green's-functions, is a long-standing problem posing enormous challenges to numerical methods. When the spectral decomposition is obtained from Fourier transforming a time series, the Nyquist-Shannon theorem limits the frequency resolution $\Delta \omega$ according to the numerically accessible time domain size $T$ via $\Delta \omega = 2\pi/T$. In tensor network methods, increasing the domain size is exponentially hard due to the ubiquitous spread of correlations, limiting the frequency resolution and thereby restricting this ansatz class mostly to one-dimensional systems with small quasi\hyp particle velocities. Here, we show how this limitation can be overcome by augmenting the time series with complex-time Krylov states. At the example of the critical $S-1/2$ Heisenberg model and light bipolarons in the two-dimensional Su-Schrieffer-Heeger model, we demonstrate the enormous improvements in accuracy, which can be achieved using this method.

cond-mat.str-el↗

arXiv2024

Quantum Restored Symmetry Protected Topological Phases

Symmetry protected topological (SPT) phases are fundamental quantum many-body states of matter beyond Landau's paradigm. Here, we introduce the concept of quantum restored SPTs (QRSPTs), where the protecting symmetry is spontaneously broken at each instance in time, but restored after time average over quantum fluctuations, so that topological features re-emerge. To illustrate the concept, we study a one-dimensional fermionic Su-Schrieffer-Heeger model with fluctuating superconducting order. We solve this problem in several limiting cases using a variety of analytical methods and compare them to numerical (density matrix renormalization group) simulations which are valid throughout the parameter regime. We thereby map out the phase diagram and identify a QRSPT phase with topological features which are reminiscent from (but not identical to) the topology of the underlying free fermion system. The QRSPT paradigm thereby stimulates a new perspective for the constructive design of novel topological quantum many-body phases.

cond-mat.str-el↗

arXiv2024

Photo-induced dynamics with continuous and discrete quantum baths

The ultrafast quantum dynamics of photophysical processes in complex molecules is an extremely challenging computational problem with a wide variety of fascinating applications in quantum chemistry and biology. Inspired by recent developments in open quantum systems, we introduce a pure-state unraveled hybrid-bath method that describes a continuous environment via a set of discrete, effective bosonic degrees of freedom using a Markovian embedding. Our method is capable of describing both, a continuous spectral density and sharp peaks embedded into it. Thereby, we overcome the limitations of previous methods, which either capture long-time memory effects using the unitary dynamics of a set of discrete vibrational modes or use memoryless Markovian environments employing a Lindblad or Redfield master equation. We benchmark our method against two paradigmatic problems from quantum chemistry and biology. We demonstrate that compared to unitary descriptions, a significantly smaller number of bosonic modes suffices to describe the excitonic dynamics accurately, yielding a computational speed-up of nearly an order of magnitude. Furthermore, we take into account explicitly the effect of a $\delta$-peak in the spectral density of a light-harvesting complex, demonstrating the strong impact of the long-time memory of the environment on the dynamics.

quant-ph↗

arXiv2024

A logical qubit-design with geometrically tunable error-resistibility

Breaking the error-threshold would mark a milestone in establishing quantum advantage for a wide range of relevant problems. One possible route is to encode information redundantly in a logical qubit by combining several noisy qubits, providing an increased robustness against external perturbations. We propose a setup for a logical qubit built from superconducting qubits (SCQs) coupled to a microwave cavity-mode. Our design is based on a recently discovered geometric stabilizing mechanism in the Bose-Hubbard wheel (BHW), which manifests as energetically well-separated clusters of many-body eigenstates. We investigate the impact of experimentally relevant perturbations between SCQs and the cavity on the spectral properties of the BHW. We show that even in the presence of typical fabrication uncertainties, the occurrence and separation of clustered many-body eigenstates is extremely robust. Introducing an additional, frequency-detuned SCQ coupled to the cavity yields duplicates of these clusters, that can be split up by an on-site potential. We show that this allows to (i) redundantly encode two logical qubit states that can be switched and read out efficiently and (ii) can be separated from the remaining many-body spectrum via geometric stabilization. We demonstrate at the example of an X-gate that the proposed logical qubit reaches single qubit-gate fidelities $>0.999$ in experimentally feasible temperature regimes $\sim10-20\,\mathrm{mK}$.

quant-ph↗

arXiv2024

Phonon state tomography of electron correlation dynamics in optically excited solids

We introduce phonon state tomography (PST) as a diagnostic probe of electron dynamics in solids whose phonons are optically excited by a laser pulse at initial time. Using a projected-purified matrix-product states algorithm, PST decomposes the exact correlated electron-phonon wavefunction into contributions from purely electronic states corresponding to statistically typical configurations of the optically accessible phononic response, enabling a 'tomographic' reconstruction of the electronic dynamics generated by the phonons. Thus, PST may be used to diagnose electronic behavior in experiments that access only the phonon response, such as thermal diffuse x-ray and electron scattering. We study the dynamics of a metal whose infrared phonons are excited by an optical pulse at initial time and use it to simulate the sample-averaged momentum-resolved phonon occupancy and accurately reconstruct the electronic correlations. We also use PST to analyze the influence of different pulse shapes on the light-induced enhancement and suppression of electronic correlations.

cond-mat.str-el↗

arXiv2023

Matrix-product-state-based band-Lanczos solver for quantum cluster approaches

We present matrix-product state (MPS) based band Lanczos method as solver for quantum cluster methods such as the variational cluster approximation. While a na\"ive implementation of MPS as cluster solver would barely improve its range of applicability, we show that our approach makes it possible to treat cluster geometries well beyond the reach of exact diagonalization methods. The key modifications we introduce are a continuous energy truncation combined with a convergence criterion that is more robust against approximation errors introduced by the MPS representation and provides a bound to deviations in the resulting Green's function. The potential of the resulting cluster solver is demonstrated by computing the self-energy functional for the single-band Hubbard model at half filling in the strongly correlated regime, on different cluster geometries. Here, we find that only when treating large cluster sizes, observables can be extrapolated to the thermodynamic limit, which we demonstrate at the example of the staggered magnetization. Treating clusters sizes with up to $6\times 6$ sites we obtain significant improvement over the extrapolation accessible with exact diagonalization solvers when comparing to quantum Monte Carlo results. Finally, we illustrate the applicability of the MPS cluster solver to more complex models by calculating spectral properties as relevant for the electron-doped cuprate CaCuO$_2$.

cond-mat.str-el↗

arXiv2023

Detecting Hidden Order in Fractional Chern Insulators

Topological phase transitions go beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking and occur without an associated local order parameter. Instead, such transitions can be characterized by the emergence of non-local order parameters, which require measurements on extensively many particles simultaneously - an impossible venture in real materials. On the other hand, quantum simulators have demonstrated such measurements, making them prime candidates for an experimental confirmation of non-local topological order. Here, building upon the recent advances in preparing few-particle fractional Chern insulators using ultracold atoms and photons, we propose a realistic scheme for detecting the hidden off-diagonal long-range order (HODLRO) characterizing Laughlin states. Furthermore, we demonstrate the existence of this hidden order in fractional Chern insulators, specifically for the $\nu=\frac{1}{2}$-Laughlin state in the isotropic Hofstadter-Bose-Hubbard model. This is achieved by large-scale numerical density matrix renormalization group (DMRG) simulations based on matrix product states, for which we formulate an efficient sampling procedure providing direct access to HODLRO in close analogy to the proposed experimental scheme. We confirm the characteristic power-law scaling of HODLRO, with an exponent $\frac{1}{\nu} = 2$, and show that its detection requires only a few thousand snapshots. This makes our scheme realistically achievable with current technology and paves the way for further analysis of non-local topological orders, e.g. in topological states with non-Abelian anyonic excitations.

cond-mat.quant-gas↗

arXiv2023

Cooper-Paired Bipolaronic Superconductors

Light-mass bipolarons in off-diagonally coupled electron-phonon systems provide a potential route to bipolaronic high-Tc superconductivity. While there has been numerical progress in the physically relevant limit of slow phonons, more insights are needed to fully understand to what extent this mechanism survives at finite densities and in different regimes. We address these questions using advanced tensor-network methods applied to the Su-Schrieffer-Heeger model. Studying both the spectral properties of isolated bipolarons as well as the pairing correlations at small finite densities, we find evidence that the conventional picture of bipolarons as molecular bound states which undergo Bose-Einstein condensation may need to be reconsidered. Instead, our findings suggest correlation-driven formation of a fragmented condensate with spatially separated polaron pairs, stabilized by strong repulsive electron-electron interactions at moderate values of the electron-phonon coupling. These spatially modulated charge clouds exhibit pairing with a typical length-scale set by the Fermi momentum.

cond-mat.supr-con↗