Publications

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• Compactness of quantics tensor train representations of local imaginary-time propagators

  Haruto Takahashi, Rihito Sakurai, Hiroshi Shinaoka

  SciPost Phys. 18, 007 (2025) · published 8 January 2025 | Toggle abstract · pdf

  Space-time dependence of imaginary-time propagators, vital for ab initio and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X 13, 021015 (2023)]. However, the impact of system parameters, like temperature, on data size remains underexplored. This paper provides a comprehensive numerical analysis of the compactness of local imaginary-time propagators in QTT for one-time/-frequency objects and two-time/-frequency objects, considering truncation in terms of the Frobenius and maximum norms. To study worst-case scenarios, we employ random pole models, where the number of poles grows logarithmically with the inverse temperature and coefficients are random. The Green's functions generated by these models are expected to be more difficult to compress than those from physical systems. The numerical analysis reveals that these propagators are highly compressible in QTT, outperforming the state-of-the-art approaches such as intermediate representation and discrete Lehmann reprensentation. For one-time/-frequency objects and two-time/-frequency objects, the bond dimensions saturate at low temperatures, especially for truncation in terms of the Frobenius norm. We provide counting-number arguments for the saturation of bond dimensions for the one-time/-frequency objects, while the origin of this saturation for two-time/-frequency objects remains to be clarified. This paper's findings highlight the critical need for further research on the selection of truncation methods, tolerance levels, and the choice between imaginary-time and imaginary-frequency representations in practical applications.

  8 citations

• Entanglement flow in the Kane-Fisher quantum impurity problem

  Chunyu Tan, Yuxiao Hang, Stephan Haas, Hubert Saleur

  SciPost Phys. Core 8, 002 (2025) · published 8 January 2025 | Toggle abstract · pdf

  The problem of a local impurity in a Luttinger liquid, just like the anisotropic Kondo problem (of which it is technically a cousin), describes many different physical systems. As shown by Kane and Fisher, the presence of interactions profoundly modifies the physics familiar from Fermi liquid theory, and leads to non-intuitive features, best described in the Renormalization Group language (RG), such as flows towards healed or split fixed points. While this problem has been studied for many years using more traditional condensed matter approaches, it remains somewhat mysterious from the point of view of entanglement, both for technical and conceptual reasons. We propose and explore in this paper a new way to think of this important aspect. We use the realization of the Kane Fisher universality class provided by an XXZ spin chain with a modified bond strength between two sites, and explore the difference of (Von Neumann) entanglement entropies of a region of length $\ell$ with the rest of the system - to which it is connected with a modified bond - in the cases when $\ell$ is even and odd. Surprisingly, we find out that this difference $\delta S\equiv S^e-S^o$ remains of $O(1)$ in the thermodynamic limit, and gives rise now, depending on the sign of the interactions, to "resonance" curves, interpolating between $-\ln 2$ and $0$, and depending on the product $\ell T_B$, where $1/T_B$ is a characteristic length scale akin to the Kondo length in Kondo problems. $\delta S$ can be interpreted as a measure of the hybridization of the left-over spin in odd length subsystems with the "bath" constituted by the rest of the chain. The problem is studied both numerically using DMRG and analytically near the healed and split fixed points. Interestingly - and in contrast with what happens in other impurity problems - $\delta S$ can, at least to lowest order, be tackled by conformal perturbation theory.

• Dynamics of systems with varying number of particles: From Liouville equations to general master equations for open systems

  Mauricio J. del Razo, Luigi Delle Site

  SciPost Phys. 18, 001 (2025) · published 6 January 2025 | Toggle abstract · pdf

  A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we review complementary physico-mathematical approaches of varying number of particles inspired by rather different specific numerical goals. As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics.

  1 citation

• Lack of near-sightedness principle in non-Hermitian systems

  Helene Spring, Viktor Könye, Anton R. Akhmerov, Ion Cosma Fulga

  SciPost Phys. 17, 153 (2024) · published 5 December 2024 | Toggle abstract · pdf

  The non-Hermitian skin effect is a phenomenon in which an extensive number of states accumulates at the boundaries of a system. It has been associated to nontrivial topology, with nonzero bulk invariants predicting its appearance and its position in real space. Here, we demonstrate that the non-Hermitian skin effect has weaker bulk-edge correspondence than topological insulators: when translation symmetry is broken by a single non-Hermitian impurity, skin modes are depleted at the boundary and accumulate at the impurity site, without changing any bulk invariant. Similarly, a single non-Hermitian impurity may deplete the states from a region of Hermitian bulk.

  3 citations

• Locality of topological dynamics in Chern insulators

  Anton Markov, Diana Golovanova, Alexander Yavorsky, Alexey Rubtsov

  SciPost Phys. 17, 152 (2024) · published 5 December 2024 | Toggle abstract · pdf

  A system having macroscopic patches in different topological phases has no well-defined global topological invariant. To treat such a case, the quantities labeling different areas of the sample according to their topological state are used, dubbed local topological markers. Here we study their dynamics. We concentrate on two quantities, namely the local Chern marker and the on-site charge induced by an applied magnetic field. The first one provides the correct information about the system's topological properties, the second can be readily measured in experiment. We demonstrate that the time-dependent local Chern marker is a much more non-local object than the equilibrium one. Surprisingly, large samples driven out of equilibrium lead to a simple description of the local Chern marker's dynamics by a local continuity equation. Also, we argue that the connection between the local Chern marker and magnetic-field induced charge known in static holds out of equilibrium in some experimentally relevant systems as well. This gives a clear physical description of the marker's evolution and provides a simple recipe for experimental estimation of the topological marker's value.

• Tunable second harmonic generation in 2D materials: Comparison of different strategies

  Simone Grillo, Elena Cannuccia, Maurizia Palummo, Olivia Pulci, Claudio Attaccalite

  SciPost Phys. Core 7, 081 (2024) · published 4 December 2024 | Toggle abstract · pdf

  Nonlinear optical frequency conversion, where optical fields interact with a nonlinear medium to generate new frequencies, is a key phenomenon in modern photonic systems. However, a major challenge with these techniques lies in the difficulty of tuning the nonlinear electrical susceptibilities that drive such effects in a given material. As a result, dynamic control of optical nonlinearities has remained largely confined to research laboratories, limiting its practical use as a spectroscopic tool. In this work, we aim to advance the development of devices with tunable nonlinear responses by exploring two potential mechanisms for electrically manipulating second-order optical nonlinearity in two-dimensional materials. Specifically, we consider two configurations: in the first, the material does not inherently exhibit second-harmonic generation (SHG), but this response is induced by an external field; in the second, an external field induces doping in a material that already exhibits SHG, altering the intensity of the nonlinear signal. In this work, we have studied these two configurations using a real-time ab-initio approach under an out-of-plane external field and including the effects of doping-induced variations in the screened electron-electron interaction. We then discuss the limitations of current computational methods and compare our results with experimental measurements.

  2 citations

• Unambiguous simulation of diffusive charge transport in disordered nanoribbons

  Henrique Pina Veiga, Simão Meneses João, João Manuel Alendouro Pinho, João Pedro Santos Pires, João Manuel Viana Parente Lopes

  SciPost Phys. 17, 149 (2024) · published 3 December 2024 | Toggle abstract · pdf

  Charge transport in disordered two-dimensional (2D) systems showcases a myriad of unique phenomenologies that highlight different aspects of the underlying quantum dynamics. Electrons in such systems undergo a crossover from ballistic propagation to Anderson localization, contingent on the system's effective coherence length. Between the extended and localized phases lies a diffusive crossover in which the charge conductivity is properly defined. The numerical observation of this regime has remained elusive because it requires fully coherent transport to be simulated in systems whose dimensions are sufficiently large to meaningfully split the mean-free path and localization length scales. To address this challenge, we employed a novel linear scaling time-resolved approach that enabled us to derive the dc-transport characteristics and observe the three expected 2D transport regimes — ballistic, diffusive, and localized.

  1 citation

• Kernel polynomial method for linear spin wave theory

  Harry Lane, Hao Zhang, David Dahlbom, Sam Quinn, Rolando D. Somma, Martin Mourigal, Cristian D. Batista, Kipton Barros

  SciPost Phys. 17, 145 (2024) · published 26 November 2024 | Toggle abstract · pdf

  Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially in systems with large magnetic unit cells, such as those with incommensurate magnetic structures or quenched disorder. In this paper, we demonstrate an efficient scheme based on the kernel polynomial method for calculating dynamical correlations of relevance to inelastic neutron scattering experiments. This method reduces the scaling of numerical cost from cubic to linear in the magnetic unit cell size.

  3 citations

• $\mathbb{Z}_4$ transitions in quantum loop models on a zig-zag ladder

  Bowy M. La Rivière, Natalia Chepiga

  SciPost Phys. 17, 144 (2024) · published 26 November 2024 | Toggle abstract · pdf

  We study the nature of quantum phase transitions out of $\mathbb{Z}_4$ ordered phases in quantum loop models on a zig-zag ladder. We report very rich critical behavior that includes a pair of Ising transitions, a multi-critical Ashkin-Teller point and a remarkably extended interval of a chiral transition. Although plaquette states turn out to be essential to realize chiral transitions, we demonstrate that critical regimes can be manipulated by deforming the model as to increase the presence of leg-dimerized states. This can be done to the point where the chiral transition turns into first order, we argue that this is associated with the emergence of a critical end point.

  2 citations

• Tensor network Python (TeNPy) version 1

  Johannes Hauschild, Jakob Unfried, Sajant Anand, Bartholomew Andrews, Marcus Bintz, Umberto Borla, Stefan Divic, Markus Drescher, Jan Geiger, Martin Hefel, Kévin Hémery, Wilhelm Kadow, Jack Kemp, Nico Kirchner, Vincent S. Liu, Gunnar Möller, Daniel Parker, Michael Rader, Anton Romen, Samuel Scalet, Leon Schoonderwoerd, Maximilian Schulz, Tomohiro Soejima, Philipp Thoma, Yantao Wu, Philip Zechmann, Ludwig Zweng, Roger S. K. Mong, Michael P. Zaletel, Frank Pollmann

  SciPost Phys. Codebases 41 (2024) · published 26 November 2024 | Toggle abstract · pdf

  TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for new-comers, while at the same time providing powerful algorithms for experts. The focus is on MPS algorithms for 1D and 2D lattices, such as DMRG ground state search, as well as dynamics using TEBD, TDVP, or MPO evolution. This article is a companion to the recent version 1.0 release of TeNPy and gives a brief overview of the package.

  16 citations