Publications

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Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

Francisco M. O. Brito, Aires Ferreira

SciPost Phys. Core 7, 006 (2024) · published 21 February 2024 | · pdf

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.
Spin-$s$ $Q$-systems: Twist and open boundaries

Yi-Jun He, Jue Hou, Yi-Chao Liu, Zi-Xi Tan

SciPost Phys. Core 8, 057 (2025) · published 27 August 2025 | · pdf

In integrable spin chains, the spectral problem can be solved by the method of Bethe Ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations. In this work, we systematically investigate the spin-$s$ XXX chain with twisted and open boundary conditions using the rational $Q$-system, which is a powerful tool to solve Bethe equations. We establish basic frameworks of the rational $Q$-system and confirm its completeness numerically in both cases. For twisted boundaries, we investigate the polynomiality conditions of the rational $Q$-system and derive physical conditions for singular solutions of Bethe equations. For open boundaries, we uncover novel phenomena such as hidden symmetries and boundary induced strings under specific boundary parameters. Hidden symmetries lead to the appearance of extra degeneracies in the Hilbert space, while the boundary induced string is a novel type of exact string configuration, whose length depends on the boundary magnetic fields. These findings, supported by both analytical and numerical evidences, offer new insights into the interplay between symmetries and boundary conditions.
On the interactions and equilibrium between Einstein-Maxwell-dilaton black holes

Ulrich K. Beckering Vinckers, Tomás Ortín

SciPost Phys. Core 8, 044 (2025) · published 17 June 2025 | · pdf

We study the interactions and the conditions for the equilibrium of forces between generic non-rotating black holes of the Einstein–Maxwell–dilaton (EMD) theory. We study known (and some new) solutions of the time-symmetric initial-data problem describing an arbitrary number of those black holes, some of them with primary scalar hair. We show how one can distinguish between initial data corresponding to dynamical situations in which the black holes (one or many) are not in equilibrium and initial data which are just constant-time slices of a static solution of the full equations of motion describing static black holes using (self-)interaction energies. For a single black hole, non-vanishing self-interaction energy is always related to primary scalar hair and to a dynamical black hole. Removing the self-interaction energies in multi-center solutions we get interaction energies related to the attractive and repulsive forces acting on the black holes. As shown by Brill and Lindquist, for widely separated black holes, these take the standard Newtonian and Coulombian forms plus an additional interaction term associated with the scalar charges which is attractive for like charges.
Spectral solutions for the Schrödinger equation with a regular singularity

Pushkar Mohile, Ayaz Ahmed, T. R. Vishnu, Pichai Ramadevi

SciPost Phys. Core 7, 041 (2024) · published 5 July 2024 | · pdf

We propose a modification in the Bethe-like ansatz to reproduce the hydrogen atom spectrum and the wave functions. Such a proposal provided a clue to attempt the exact quantization condition (EQC) for the quantum periods associated with potentials $V(x)$ which are of the form $(V(x) = |x| + a/|x| + b/|x|^2 )$. We validate the EQC proposal by showing that our computed Voros spectrum in the limit $a,b → 0$ is matching well with the true spectrum of the familiar $|x|$ potential. Thus we have given a route to obtain the spectral solution for the one dimensional Schrödinger equation involving potentials with regular singularity at the origin.
Anyon condensation in mixed-state topological order

Ken Kikuchi, Kah-Sen Kam, Fu-Hsiang Huang

SciPost Phys. Core 8, 072 (2025) · published 20 October 2025 | · pdf

We discuss anyon condensation in mixed-state topological order. The phases were recently conjectured to be classified by pre-modular fusion categories. Just like anyon condensation in pure-state topological order, a bootstrap analysis shows condensable anyons are given by connected étale algebras. We explain how to perform generic anyon condensation including non-invertible anyons and successive condensations. Interestingly, some condensations lead to pure-state topological orders. We clarify when this happens. We also compute topological invariants of equivalence classes.
Digital quantum simulation of bosonic systems and quantum complementarity

Victor P. Brasil, Diego S. Starke, Jonas Maziero

SciPost Phys. Core 8, 086 (2025) · published 24 November 2025 | · pdf

Digital quantum simulation (DQS) has emerged as a powerful approach to investigate complex quantum systems using digital quantum computers. Such systems, like many-particle bosonic systems and intricate optical experimental setups, pose significant challenges for classical simulation methods. In this paper, we utilize a general formalism for the DQS of bosonic systems, which consists of mapping bosonic operators to Pauli operators using the Gray code, in order to simulate interferometric variants of Afshar's experiment—an intricate optical experiment—on IBM's quantum computers. We investigated experiments analogous to Afshar's double-slit experiment performed by Unruh and Pessoa Júnior, exploring discussions on the apparent violation of Bohr's complementarity principle when considering the entire experimental setup. Based on the aforementioned experiments, we construct a variation of a delayed-choice setup. We also explore another experiment starting with a two-photon initial state. Finally, we analyze these experiments within the framework of an updated quantum complementarity principle, which applies to specific quantum state preparations and remains consistent with the foundational principles of Quantum Mechanics.
The fermionic double smeared null energy condition

Duarte Fragoso, Lihan Guo

SciPost Phys. Core 8, 045 (2025) · published 26 June 2025 | · pdf

Energy conditions are crucial for understanding why exotic phenomena such as traversable wormholes and closed timelike curves remain elusive. In this paper, we prove the Double Smeared Null Energy Condition (DSNEC) for the fermionic free theory in 4-dimensional flat Minkowski spacetime, extending previous work on the same energy condition for the bosonic case [J. R. Fliss and B. Freivogel, SciPost Phys. 12, 084 (2022); J. R. Fliss et al., SciPost Phys. 14, 024 (2023)] by adapting Fewster and Mistry's method [C. J. Fewster and B. Mistry, Phys. Rev. D 68, 105010 (2003)] to the energy-momentum tensor $T_{++}$. A notable difference from previous works lies in the presence of the $\gamma_0 \gamma_+$ matrix in $T_{++}$, causing a loss of symmetry. This challenge is addressed by making use of its square-root matrix. We provide explicit analytic results for the massless case as well as numerical insights for the mass-dependence of the bound in the case of Gaussian smearing.
Learning selection cuts with gradients

Mike Hance, Juan Robles

SciPost Phys. Core 8, 079 (2025) · published 7 November 2025 | · pdf

Many analyses in high-energy physics rely on selection thresholds (cuts) applied to detector, particle, or event properties. Initial cut values can often be guessed from physical intuition, but cut optimization, especially for multiple features, is commonly performed by hand, or skipped entirely in favor of multivariate algorithms like BDTs or neural networks. We revisit this problem, and develop a cut optimization approach based on gradient descent. Cut thresholds are learned as parameters of a network with a simple architecture, and can be tuned to achieve a target signal efficiency through the use of custom loss functions. Contractive terms in the loss can be used to ensure a smooth evolution of cuts as functions of efficiency, particle kinematics, or event features. The method is used to classify events in a search for Supersymmetry, and the performance is compared with common classification tools. An implementation of this approach is available in a public code repository and python package.
A linear algebra-based approach to understanding the relation between the winding number and zero-energy edge states

Chen-Shen Lee

SciPost Phys. Core 7, 003 (2024) · published 30 January 2024 | · pdf

The one-to-one relation between the winding number and the number of robust zero-energy edge states, known as bulk-boundary correspondence, is a celebrated feature of 1$d$ systems with chiral symmetry. Although this property can be explained by the K-theory, the underlying mechanism remains elusive. Here, we demonstrate that, even without resorting to advanced mathematical techniques, one can prove this correspondence and clearly illustrate the mechanism using only Cauchy's integral and elementary algebra. Furthermore, our approach to proving bulk-boundary correspondence also provides clear insights into a kind of system that doesn't respect chiral symmetry but can have robust left or right zero-energy edge states. In such systems, one can still assign the winding number to characterize these zero-energy edge states.
Necklace Ansatz for strongly repulsive spin mixtures on a ring

Gianni Aupetit-Diallo, Giovanni Pecci, Artem Volosniev, Mathias Albert, Anna Minguzzi, Patrizia Vignolo

SciPost Phys. Core 8, 022 (2025) · published 14 February 2025 | · pdf

We propose an alternative to the Bethe Ansatz method for repulsive strongly-interacting fermionic (or bosonic) mixtures on a ring. Starting from the knowledge of the solution for single-component non-interacting fermions (or strongly-interacting bosons), we explicitly impose periodic condition on the amplitudes of the spin configurations. This reduces drastically the number of independent complex amplitudes that we determine by constrained diagonalization of an effective Hamiltonian. This procedure allows us to obtain a complete basis for the exact low-energy many-body solutions for mixtures with a large number of particles, both for $SU(\kappa)$ and symmetry-breaking systems.

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