Publications

Order by: publication date number of citations

• Non-equilibrium dynamics of dipolar polarons

  Artem G. Volosniev, Giacomo Bighin, Luis Santos, Luis A. Peña Ardila

  SciPost Phys. 15, 232 (2023) · published 7 December 2023 | Toggle abstract · pdf

  We study the out-of-equilibrium quantum dynamics of dipolar polarons, i.e., impurities immersed in a dipolar Bose-Einstein condensate, after a quench of the impurity-boson interaction. We show that the dipolar nature of the condensate and of the impurity results in anisotropic relaxation dynamics, in particular, anisotropic dressing of the polaron. More relevantly for cold-atom setups, quench dynamics is strongly affected by the interplay between dipolar anisotropy and trap geometry. Our findings pave the way for simulating impurities in anisotropic media utilizing experiments with dipolar mixtures.

  1 citation

• A new integrable structure associated to the Camassa-Holm peakons

  Jean Avan, Luc Frappat, Eric Ragoucy

  SciPost Phys. 15, 228 (2023) · published 6 December 2023 | Toggle abstract · pdf

  We provide a closed Poisson algebra involving the Ragnisco-Bruschi generalization of peakon dynamics in the Camassa-Holm shallow-water equation. This algebra is generated by three independent matrices. From this presentation, we propose a one-parameter integrable extension of their structure. It leads to a new $N$-body peakon solution to the Camassa-Holm shallow-water equation depending on two parameters. We present two explicit constructions of a (non-dynamical) $r$-matrix formulation for this new Poisson algebra. The first one relies on a tensorization of the $N$-dimensional auxiliary space by a 4-dimensional space. We identify a family of Poisson commuting quantities in this framework, including the original ones. This leads us to constructing a second formulation identified as a spectral parameter representation.

  1 citation

• Residual matrix product state for machine learning

  Ye-Ming Meng, Jing Zhang, Peng Zhang, Chao Gao, Shi-Ju Ran

  SciPost Phys. 14, 142 (2023) · published 2 June 2023 | Toggle abstract · pdf

  Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network models for classical machine learning. In this work, we combine the ideas of matrix product state (MPS), the simplest tensor network structure, and residual neural network and propose the residual matrix product state (ResMPS). The ResMPS can be treated as a network where its layers map the "hidden" features to the outputs (e.g., classifications), and the variational parameters of the layers are the functions of the features of the samples (e.g., pixels of images). This is different from neural network, where the layers map feed-forwardly the features to the output. The ResMPS can equip with the non-linear activations and dropout layers, and outperforms the state-of-the-art tensor network models in terms of efficiency, stability, and expression power. Besides, ResMPS is interpretable from the perspective of polynomial expansion, where the factorization and exponential machines naturally emerge. Our work contributes to connecting and hybridizing neural and tensor networks, which is crucial to further enhance our understanding of the working mechanisms and improve the performance of both models.

  1 citation

• Thermal pure matrix product state in two dimensions: Tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state

  Matthias Gohlke, Atsushi Iwaki, Chisa Hotta

  SciPost Phys. 15, 206 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We present the first successful application of the matrix product state (MPS) representing a thermal quantum pure state (TPQ) in equilibrium in two spatial dimensions over almost the entire temperature range. We use the Kitaev honeycomb model as a prominent example hosting a quantum spin liquid (QSL) ground state to target the two specific-heat peaks previously solved nearly exactly using the free Majorana fermionic description. Starting from the high-temperature random state, our TPQ-MPS framework on a cylinder precisely reproduces these peaks, showing that the quantum many-body description based on spins can still capture the emergent itinerant Majorana fermions in a ${\mathbb Z}_2$ gauge field. The truncation process efficiently discards the high-energy states, eventually reaching the long-range entangled topological state approaching the exact ground state for a given finite size cluster. An advantage of TPQ-MPS over exact diagonalization or purification-based methods is its lowered numerical cost coming from a reduced effective Hilbert space even at finite temperature.

  1 citation

• Benchmarking the Ising universality class in $3 \le d < 4$ dimensions

  Claudio Bonanno, Andrea Cappelli, Mikhail Kompaniets, Satoshi Okuda, Kay Joerg Wiese

  SciPost Phys. 14, 135 (2023) · published 30 May 2023 | Toggle abstract · pdf

  The Ising critical exponents $\eta$, $\nu$ and $\omega$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.

  1 citation

• Gravitational multipoles in general stationary spacetimes

  Daniel R. Mayerson

  SciPost Phys. 15, 154 (2023) · published 11 October 2023 | Toggle abstract · pdf

  The Geroch-Hansen and Thorne (ACMC) formalisms give rigorous and equivalent definitions for gravitational multipoles in stationary vacuum spacetimes. However, despite their ubiquitous use in gravitational physics, it has not been shown that these formalisms can be generalized to non-vacuum stationary solutions, except in a few special cases. This paper shows how the Geroch-Hansen formalism can be generalized to arbitrary non-vacuum stationary spacetimes for metrics that are sufficiently smooth at infinity. The key is the construction of an improved twist vector, which is well-defined under a mild topological condition on the spacetime (which is automatically satisfied for black holes). Ambiguities in the construction of this improved twist vector are discussed and fixed by imposing natural "gauge fixing" conditions, which also immediately lead to the equivalence between the Geroch-Hansen and Thorne formalisms for such arbitrary stationary spacetimes.

  1 citation

• Integrable quadratic structures in peakon models

  J. Avan, L. Frappat, E. Ragoucy

  SciPost Phys. 13, 044 (2022) · published 31 August 2022 | Toggle abstract · pdf

  We propose realizations of the Poisson structures for the Lax representations of three integrable $n$-body peakon equations, Camassa--Holm, Degasperis--Procesi and Novikov. The Poisson structures derived from the integrability structures of the continuous equations yield quadratic forms for the $r$-matrix representation, with the Toda molecule classical $r$-matrix playing a prominent role. We look for a linear form for the $r$-matrix representation. Aside from the Camassa--Holm case, where the structure is already known, the two other cases do not allow such a presentation, with the noticeable exception of the Novikov model at $n=2$. Generalized Hamiltonians obtained from the canonical Sklyanin trace formula for quadratic structures are derived in the three cases.

  1 citation

• Microcanonical and canonical fluctuations in atomic Bose-Einstein condensates – Fock state sampling approach

  Maciej Bartłomiej Kruk, Dawid Hryniuk, Mick Kristensen, Toke Vibel, Krzysztof Pawłowski, Jan Arlt, Kazimierz Rzążewski

  SciPost Phys. 14, 036 (2023) · published 16 March 2023 | Toggle abstract · pdf

  The fluctuations of the atom number between a Bose-Einstein condensate and the surrounding thermal gas have been the subject of a long standing theoretical debate. This discussion is centered around the appropriate thermodynamic ensemble to be used for theoretical predictions and the effect of interactions on the observed fluctuations. Here we introduce the so-called Fock state sampling method to solve this classic problem of current experimental interest for weakly interacting gases. A suppression of the predicted peak fluctuations is observed when using a microcanonical with respect to a canonical ensemble. Moreover, interactions lead to a shift of the temperature of peak fluctuations for harmonically trapped gases. The absolute size of the fluctuations furthermore depends on the total number of atoms and the aspect ratio of the trapping potential. Due to the interplay of these effect, there is no universal suppression or enhancement of fluctuations.

  1 citation

• Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation

  B. Pahlevanzadeh, P. Sahebsara, D. Sénéchal

  SciPost Phys. 13, 040 (2022) · published 30 August 2022 | Toggle abstract · pdf

  We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek, relevant to a twist angle of $1.30^\circ$, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion $U$ is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.

  1 citation

• Electric polarization and magnetization in metals

  Perry T. Mahon, John E. Sipe

  SciPost Phys. 14, 058 (2023) · published 3 April 2023 | Toggle abstract · pdf

  A feature of the "modern theory" is that electric polarization is not well-defined in a metallic ground state. A different approach invokes the general existence of a complete set of exponentially localized Wannier functions, with respect to which general definitions of microscopic electronic polarization and magnetization fields, and free charge and current densities are always admitted. These definitions assume no particular initial electronic state of the crystal, and the set of microscopic fields satisfy the usual relations of classical electrodynamics. Notably, when applied to a trivial insulator initially occupying its $T=0$ ground state, the expressions for the unperturbed polarization and orbital magnetization, and for the orbital magnetoelectric polarizability tensor obtained from these different approaches can agree. However, the "modern theory of magnetization" has been extended via thermodynamic arguments to include metals and Chern insulators. We here compare with that generalization and find disagreement; the manner in which the expressions differ elucidates the distinct philosophies of these approaches. Our approach leads to the usual electrical conductivity tensor in the long-wavelength limit; in the absence of any scattering mechanisms, the dc divergence of that tensor is due to the free current density and the finite-frequency generalization of the anomalous Hall contribution arises from a combination of bound and free current densities. As well, in the limit that the electronic ground state is that of a trivial insulator, our expressions reduce to those expected for the unperturbed polarization and magnetization, and the electric susceptibility.

  1 citation