Publications

Order by: publication date number of citations

• Learning tensor networks with tensor cross interpolation: New algorithms and libraries

  Yuriel Núñez Fernández, Marc K. Ritter, Matthieu Jeannin, Jheng-Wei Li, Thomas Kloss, Thibaud Louvet, Satoshi Terasaki, Olivier Parcollet, Jan von Delft, Hiroshi Shinaoka, Xavier Waintal

  SciPost Phys. 18, 104 (2025) · published 20 March 2025 | Toggle abstract · pdf

  The tensor cross interpolation (TCI) algorithm is a rank-revealing algorithm for decomposing low-rank, high-dimensional tensors into tensor trains/matrix product states (MPS). TCI learns a compact MPS representation of the entire object from a tiny training data set. Once obtained, the large existing MPS toolbox provides exponentially fast algorithms for performing a large set of operations. We discuss several improvements and variants of TCI. In particular, we show that replacing the cross interpolation by the partially rank-revealing LU decomposition yields a more stable and more flexible algorithm than the original algorithm. We also present two open source libraries, xfac in Python/C++ and TensorCrossInterpolation.jl in Julia, that implement these improved algorithms, and illustrate them on several applications. These include sign-problem-free integration in large dimension, the "superhigh-resolution" quantics representation of functions, the solution of partial differential equations, the superfast Fourier transform, the computation of partition functions, and the construction of matrix product operators.

  19 citations

• Statistical mechanics of exponentially many low lying states

  Swapnamay Mondal

  SciPost Phys. 18, 103 (2025) · published 19 March 2025 | Toggle abstract · pdf

  It has recently been argued that for near-extremal black holes, the entropy and the energy above extremality respectively receive a $log T$ and a $T$-linear correction, where $T$ is the temperature. We show that both these features can be derived in a "low but not too low" temperature regime, by assuming the existence of exponentially many low lying states cleanly separated from rest of the spectrum, without using any specific theory. Argument of the logarithm in the expression of entropy is seen to be the ratio of temperature and the bandwidth of the low lying states. We argue that such spectrum might arise in non-supersymmetric extremal brane systems. Our findings strengthen Page's suggestion that there is no true degeneracy for non-supersymmetric extremal black holes.

• Conformal geometry from entanglement

  Isaac H. Kim, Xiang Li, Ting-Chun Lin, John McGreevy, Bowen Shi

  SciPost Phys. 18, 102 (2025) · published 19 March 2025 | Toggle abstract · pdf

  In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities $(\mathfrak{c}_{\textrm{tot}}, \eta)$ that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity $\mathfrak{c}_{\textrm{tot}}$ is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) $\mathfrak{c}_{\textrm{tot}}$ is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) $\eta$ is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. We show that stationarity of $\mathfrak{c}_{\textrm{tot}}$ is equivalent to a vector fixed-point equation involving $\eta$, making our assumption locally checkable. We also derive similar results for 1+1D systems under a suitable set of assumptions.

  1 citation

• Trans-series from condensates

  Marcos Mariño, Ramon Miravitllas

  SciPost Phys. 18, 101 (2025) · published 19 March 2025 | Toggle abstract · pdf

  The Shifman–Vainshtein–Zakharov (SVZ) sum rules provide a method to obtain trans-series expansions in many quantum field theories, in which exponentially small corrections are calculated by combining the operator product expansion with the assumption of vacuum condensates. In some solvable models, exact expressions for trans-series can be obtained from non-perturbative results, and this makes it possible to test the SVZ method by comparing its predictions to these exact trans-series. In this paper we perform such a precision test in the example of the fermion self-energy in the Gross–Neveu model. Its exact trans-series expansion can be extracted from the large $N$ solution, at the first non-trivial order in $1/N$. It is given by an infinite series of exponentially small corrections involving factorially divergent power series in the 't Hooft parameter. We show that the first two corrections are associated to two-quark and four-quark condensates, and we reproduce the corresponding power series exactly, and at all loops, by using the SVZ method. In addition, the numerical values of the condensates can be extracted from the exact result, up to order $1/N$.

  1 citation

• Boundary time crystals as AC sensors: Enhancements and constraints

  Dominic Gribben, Anna Sanpera, Rosario Fazio, Jamir Marino, Fernando Iemini

  SciPost Phys. 18, 100 (2025) · published 18 March 2025 | Toggle abstract · pdf

  We investigate the use of a boundary time crystals (BTCs) as quantum sensors of AC fields. Boundary time crystals are non-equilibrium phases of matter in contact to an environment, for which a macroscopic fraction of the many-body system breaks the time translation symmetry. We find an enhanced sensitivity of the BTC when its spins are resonant with the applied AC field, as quantified by the quantum Fisher information (QFI). The QFI dynamics in this regime is shown to be captured by a relatively simple Ansatz consisting of an initial power-law growth and late-time exponential decay. We study the scaling of the Ansatz parameters with resources (encoding time and number of spins) and identify a moderate quantum enhancement in the sensor performance through comparison with classical QFI bounds. Investigating the precise source of this performance, we find that despite of its long coherence time and multipartite correlations (advantageous properties for quantum metrology), the entropic cost of the BTC (which grows indefinitely in the thermodynamic limit) hinders an optimal decoding of the AC field information. This result has implications for future candidates of quantum sensors in open system and we hope it will encourage future study into the role of entropy in quantum metrology.

  6 citations

• Molecular sorting on a fluctuating membrane

  Damiano Andreghetti, Luca Dall'Asta, Andrea Gamba, Igor Kolokolov, Vladimir Lebedev

  SciPost Phys. 18, 099 (2025) · published 18 March 2025 | Toggle abstract · pdf

  Molecular sorting in biological membranes is essential for proper cellular function. It also plays a crucial role in the budding of enveloped viruses from host cells. We recently proposed that this process is driven by phase separation, where the formation and growth of sorting domains depend primarily on direct intermolecular interactions. In addition to these, Casimir-like forces—arising from entropic effects in fluctuating membranes —may also play a significant role in the molecular distillation process. Here, using a combination of theoretical analysis and numerical simulations, we explore how Casimir-like forces between rigid membrane inclusions contribute to sorting, particularly in the biologically relevant regime where direct intermolecular interactions are weak. Our results show that these forces enhance molecular distillation by reducing the critical radius for the formation of new sorting domains and facilitating the capture of molecules within these domains. We identify the relative rigidity of the membrane and supermolecular domains as a key parameter controlling molecular sorting efficiency, offering new insights into the physical principles underlying molecular sorting in biological systems.

  1 citation

• Chiral adiabatic transmission protected by Fermi surface topology

  Isidora Araya Day, Kostas Vilkelis, Antonio L. R. Manesco, Ahmet Mert Bozkurt, Valla Fatemi, Anton R. Akhmerov

  SciPost Phys. 18, 098 (2025) · published 18 March 2025 | Toggle abstract · pdf

  We demonstrate that Andreev modes that propagate along a transparent Josephson junction have a perfect transmission at the point where three junctions meet. The chirality and the number of quantized transmission channels is determined by the topology of the Fermi surface and the vorticity of the superconducting phase differences at the trijunction. We explain this chiral adiabatic transmission (CAT) as a consequence of the adiabatic evolution of the scattering modes both in momentum and real space. The dispersion relation of the junction then separates the scattering trajectories by introducing inaccesible regions of phase space. We expect that CAT is observable in nonlocal conductance and thermal transport measurements. Furthermore, because it does not rely on particle-hole symmetry, CAT is also possible to observe directly in metamaterials.

• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries

  Heidar Moradi, Ömer M. Aksoy, Jens H. Bardarson, Apoorv Tiwari

  SciPost Phys. 18, 097 (2025) · published 17 March 2025 | Toggle abstract · pdf

  We investigate the gauging of higher-form finite Abelian symmetries and their sub-groups in quantum spin models in spatial dimensions $d=2$ and 3. Doing so, we naturally uncover gauged models with dual higher-group symmetries and potential mixed ‘t Hooft anomalies. We demonstrate that the mixed anomalies manifest as the symmetry fractionalization of higher-form symmetries participating in the mixed anomaly. Gauging is realized as an isomorphism or duality between the bond algebras that generate the space of quantum spin models with the dual generalized symmetry structures. We explore the mapping of gapped phases under such gauging related dualities for 0-form and 1-form symmetries in spatial dimension $d=2$ and 3. In $d=2$, these include several non-trivial dualities between short-range entangled gapped phases with 0-form symmetries and 0-form symmetry enriched Higgs and (twisted) deconfined phases of the gauged theory with possible symmetry fractionalizations. Such dualities also imply strong constraints on several unconventional, i.e., deconfined or topological transitions. In $d=3$, among others, we find, dualities between topological orders via gauging of 1-form symmetries. Hamiltonians self-dual under gauging of 1-form symmetries host emergent non-invertible symmetries, realizing higher-categorical generalizations of the Tambara-Yamagami fusion category.

  6 citations

• Generative learning of continuous data by tensor networks

  Alex Meiburg, Jing Chen, Jacob Miller, Raphaëlle Tihon, Guillaume Rabusseau, Alejandro Perdomo-Ortiz

  SciPost Phys. 18, 096 (2025) · published 17 March 2025 | Toggle abstract · pdf

  Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable features arising from their quantum-inspired nature, tensor network generative models have previously been largely restricted to binary or categorical data, limiting their utility in real-world modeling problems. We overcome this by introducing a new family of tensor network generative models for continuous data, which are capable of learning from distributions containing continuous random variables. We develop our method in the setting of matrix product states, first deriving a universal expressivity theorem proving the ability of this model family to approximate any reasonably smooth probability density function with arbitrary precision. We then benchmark the performance of this model on several synthetic and real-world datasets, finding that the model learns and generalizes well on distributions of continuous and discrete variables. We develop methods for modeling different data domains, and introduce a trainable compression layer which is found to increase model performance given limited memory or computational resources. Overall, our methods give important theoretical and empirical evidence of the efficacy of quantum-inspired methods for the rapidly growing field of generative learning.

  2 citations

• Space-time first-order correlations of an open Bose Hubbard model with incoherent pump and loss

  Martina Zündel, Leonardo Mazza, Léonie Canet, Anna Minguzzi

  SciPost Phys. 18, 095 (2025) · published 17 March 2025 | Toggle abstract · pdf

  We investigate the correlation properties in the steady state of driven-dissipative interacting bosonic systems in the quantum regime, as for example non-linear photonic cavities. Specifically, we consider the Bose-Hubbard model on a periodic chain and with spatially homogeneous one-body loss and pump within the Markovian approximation. The steady state is non-thermal and is formally equivalent to an infinite-temperature state with finite chemical potential set by the dissipative parameters. While there is no effect of interactions on the steady state, we observe a nontrivial behaviour of the space-time two-point correlation function, obtained by exact diagonalisation. In particular, we find that the decay width of the propagator is not only renormalised at increasing interactions, as it is the case of a single non-linear resonator, but also at increasing hopping strength. Furthermore, we numerically predict at large interactions a plateau value of the decay rate which goes beyond perturbative results in the interaction strength. We then compute the full spectral function, finding that it contains both a dispersive free-particle like dispersion at low energy and a doublon branch at energy corresponding to the on-site interactions. We compare with the corresponding calculation for the ground state of a closed quantum system and show that the driven-dissipative nature – determining both the steady state and the dynamical evolution – changes the low-lying part of the spectrum, where noticeably, the dispersion is quadratic instead of linear at small wavevectors. Finally, we compare to a high temperature grand-canonical equilibrium state and show the difference with respect to the open system stemming from the additional degree of freedom of the dissipation that allows one to vary the width of the dispersion lines.

  1 citation