Publications

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Gaussian state approximation of quantum many-body scars

Wouter Buijsman, Yevgeny Bar Lev

SciPost Phys. 17, 055 (2024) · published 15 August 2024 | · pdf

Quantum many-body scars are atypical, highly nonthermal eigenstates embedded in a sea of thermal eigenstates that have been observed in, for example, kinetically constrained quantum many-body models. These special eigenstates are characterized by a bipartite entanglement entropy that scales as most logarithmically with the subsystem size. We use numerical optimization techniques to investigate if quantum many-body scars of the experimentally relevant PXP model can be well approximated by Gaussian states. Gaussian states are described by a number of parameters that scales quadratically with system size, thereby having a much lower complexity than generic quantum many-body states, for which this number scales exponentially. We find that while quantum many-body scars can typically be well approximated by (symmetrized) Gaussian states, this is not the case for ergodic (thermal) eigenstates. This observation suggests that the non-ergodic part of the PXP Hamiltonian is related to certain quadratic parent Hamiltonians, thereby hinting on the origin of the quantum many-body scars.
Triplet character of 2D-fermion dimers arising from $s$-wave attraction via spin-orbit coupling and Zeeman splitting

Ulrich Ebling, Ulrich Zülicke, Joachim Brand

SciPost Phys. 12, 167 (2022) · published 19 May 2022 | · pdf

We theoretically study spin-$1/2$ fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting - a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak $s$-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and one-dimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its $p$-wave character, provide observable signatures of unconventional pairing.
Thermoelectric coefficients and the figure of merit for large open quantum dots

Robert S. Whitney, Keiji Saito

SciPost Phys. 6, 012 (2019) · published 24 January 2019 | · pdf

We consider the thermoelectric response of chaotic or disordered quantum dots in the limit of phase-coherent transport, statistically described by random matrix theory. We calculate the full distribution of the thermoelectric coefficients (Seebeck $S$ and Peltier $\Pi$), and the thermoelectric figure of merit $ZT$, for large open dots at arbitrary temperature and external magnetic field, when the number of modes in the left and right leads ($N_{\rm L}$ and $N_{\rm R}$) are large. Our results show that the thermoelectric coefficients and $ZT$ are maximal when the temperature is half the Thouless energy, and the magnetic field is negligible. They remain small, even at their maximum, but they exhibit a type of universality at all temperatures, in which they do not depend on the asymmetry between the left and right leads $(N_{\rm L}-N_{\rm R})$, even though they depend on $(N_{\rm L}+N_{\rm R})$.
Tangentially active polymers in cylindrical channels

José Martín-Roca, Emanuele Locatelli, Valentino Bianco, Paolo Malgaretti, Chantal Valeriani

SciPost Phys. 17, 107 (2024) · published 8 October 2024 | · pdf

We present an analytical and computational study characterizing the structural and dynamical properties of an active filament confined in cylindrical channels. We first outline the effects of the interplay between confinement and polar self-propulsion on the conformation of the chains. We observe that the scaling of the polymer size in the channel, quantified by the end-to-end distance, shows different anomalous behaviours under different confinement and activity conditions. In particular, we report scaling exponents that are markedly different from their passive counterparts. Interestingly, we show that the universal relation, describing the ratio between the end-to-end distance of passive polymer chains in cylindrical channels and in bulk is broken by activity. Finally, we show that the long-time diffusion coefficient under confinement can be rationalised by an analytical model, that takes into account the presence of the channel and the elongated nature of the polymer.
Fermionic defects of topological phases and logical gates

Ryohei Kobayashi

SciPost Phys. 15, 028 (2023) · published 25 July 2023 | · pdf

We discuss the codimension-1 defects of (2+1)D bosonic topological phases, where the defects can support fermionic degrees of freedom. We refer to such defects as fermionic defects, and introduce a certain subclass of invertible fermionic defects called "gauged Gu-Wen SPT defects" that can shift self-statistics of anyons. We derive a canonical form of a general fermionic invertible defect, in terms of the fusion of a gauged Gu-Wen SPT defect and a bosonic invertible defect decoupled from fermions on the defect. We then derive the fusion rule of generic invertible fermionic defects. The gauged Gu-Wen SPT defects give rise to interesting logical gates of stabilizer codes in the presence of additional ancilla fermions. For example, we find a realization of the CZ logical gate on the (2+1)D $\mathbb{Z}_2$ toric code stacked with a (2+1)D ancilla trivial atomic insulator. We also investigate a gapped fermionic interface between (2+1)D bosonic topological phases realized on the boundary of the (3+1)D Walker-Wang model. In that case, the gapped interface can shift the chiral central charge of the (2+1)D phase. Among these fermionic interfaces, we study an interesting example where the (3+1)D phase has a spatial reflection symmetry, and the fermionic interface is supported on a reflection plane that interpolates a (2+1)D surface topological order and its orientation-reversal. We construct a (3+1)D exactly solvable Hamiltonian realizing this setup, and find that the model generates the $\mathbb{Z}_8$ classification of the (3+1)D invertible phase with spatial reflection symmetry and fermion parity on the reflection plane. We make contact with an effective field theory, known in literature as the exotic invertible phase with spacetime higher-group symmetry.
Connected correlations in partitioning protocols: A case study and beyond

Saverio Bocini

SciPost Phys. 15, 027 (2023) · published 25 July 2023 | · pdf

The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address formally the question of when an observable is local enough to be described by GHD using the playground of partitioning protocols and non-interacting time evolution. We show that any state evolving under a quadratic Hamiltonian can be described via a set of decoupled dynamical fields such that one of those fields can be identified with a space-time-dependent generalisation of the root density. By studying the contribution to a connected spin correlation of each of those fields independently, we derive the locality conditions under which an observable can be described using the root density only. That shows both the regime of validity for hydrodynamic approaches that aim at describing the asymptotic value of observables in term of the root density only, such as GHD, and the locality conditions necessary for Gaussianification to occur.
Renormalization approach to the superconducting Kondo model

Steffen Sykora, Tobias Meng

SciPost Phys. 13, 016 (2022) · published 12 August 2022 | · pdf

An approach to bound states based on unitary transformations of Hamiltonians is presented. The method is applied to study the interaction between electrons in a BCS $s$-wave superconductor and a quantum spin. It is shown that known results from the t-matrix method and numerical studies are reproduced by this new method. As a main advantage, the method can straightforwardly be extended to study the topological properties of combined bound states in chains of many magnetic impurities. It also provides a uniform picture of the interplay between the Yu-Shiba-Rusinov (YSR) bound states and the Kondo singlet state.
Exact finite-size scaling of the maximum likelihood spectra in the quenched and annealed Sherrington-Kirkpatrick spin glass

Ding Wang, Lei-Han Tang

SciPost Phys. 17, 106 (2024) · published 8 October 2024 | · pdf

Fine resolution of the discrete eigenvalues at the spectral edge of an $N× N$ random matrix is required in many applications. Starting from a finite-size scaling ansatz for the Stieltjes transform of the maximum likelihood spectrum, we demonstrate that the scaling function satisfies a first-order ODE of the Riccati type. Further transformation yields a linear second-order ODE for the characteristic function, whose nodes determine leading eigenvalues. Using this technique, we examine in detail the spectral crossover of the annealed Sherrington-Kirkpatrick (SK) spin glass model, where a gap develops below a critical temperature. Our analysis provides analytic predictions for the finite-size scaling of the spin condensation phenomenon in the annealed SK model, validated by Monte Carlo simulations. Deviation of scaling amplitudes from their predicted values is observed in the critical region due to eigenvalue fluctuations. More generally, rescaling the spectral axis, adjusted to the distance of neighboring eigenvalues, offers a powerful approach to handling singularities in the infinite size limit.
Dynamic hysteresis across a dissipative multi-mode phase transition

Marvin Röhrle, Jens Benary, Erik Bernhart, Herwig Ott

SciPost Phys. 16, 158 (2024) · published 28 June 2024 | · pdf

Dissipative phase transitions are characteristic features in open quantum systems. Key signatures are the dynamical switching between different states in the vicinity of the phase transition and the appearance of hysteresis. Here, we experimentally study dynamic sweeps across a first order dissipative phase transition in a multi-mode driven-dissipative system. In contrast to previous studies, we perform sweeps of the dissipation strength instead of the driving strength. We extract exponents for the scaling of the hysteresis area in dependence of the sweep time and study the $g^{(2)}(0)$ correlations, which show non-trivial behavior. By changing the temperature of the system we investigate the importance of coherently pumping the system. We compare our results to numerical calculations done for a single mode variant of the system, and find surprisingly good agreement. Furthermore, we identify and discuss the differences between a scan of the dissipation strength and a scan of the driving strength.
Probabilistic deconstruction of a theory of gravity, part II: Curved space

Sunok Josephine Suh

SciPost Phys. 16, 012 (2024) · published 17 January 2024 | · pdf

We propose that the underlying context of holographic duality and the Ryu-Takayanagi formula is that the volume measure of spacetime is a probability measure constrained by quantum dynamics. We define quantum stochastic processes using joint quantum distributions which are realized in a quantum system as expectation values of products of projectors. In anti-de Sitter JT gravity, we show that Einstein's equations arise from the evolution of probability under the quantum stochastic process induced by the boundary, with the area of compactified space in the gravitational theory identified as a probability density evolving under the quantum process. Extrapolating these and related results in flat JT gravity found in [SciPost Phys. 15, 174 (2023)], we conjecture that general relativity arises in the semi-classical limit of the evolution of probability with respect to quantum stochastic processes.

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