Publications

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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.
Velocity gauge formulation of nonlinear optical response in Floquet quantum systems

S. Sajad Dabiri, Reza Asgari

SciPost Phys. Core 8, 049 (2025) · published 21 July 2025 | · pdf

Using the velocity gauge formalism, we develop a theoretical framework for computing the nonlinear optical responses of time-periodic quantum systems. This approach complements the length gauge formulation and offers distinct advantages in both numerical and analytical treatments, particularly for atomic and solid-state systems with well-defined momentum-space structures. By applying our framework to the Rabi model, we derive numerical solutions in the velocity gauge and compare them with the length gauge, demonstrating full agreement between the two formulations. Our findings reveal rich optical phenomena, including photon-assisted transitions, frequency mixing effects, and emergent Floquet-induced photocurrents that are absent in static systems. We demonstrate that nonlinear responses in Floquet-driven systems exhibit resonances at integer multiples of the driving frequency, providing insights into ultrafast spectroscopy and Floquet engineering of quantum materials. The present formulation establishes a bridge between theoretical models and experimental observations in driven quantum systems, with potential applications in quantum optics, photonics, and next-generation optoelectronic devices.
Tensorization of neural networks for improved privacy and interpretability

José Ramón Pareja Monturiol, Alejandro Pozas-Kerstjens, David Pérez-García

SciPost Phys. Core 8, 095 (2025) · published 24 December 2025 | · pdf

We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the MPS representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing MPS in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.
Entanglement classification via operator size

Qi-Feng Wu

SciPost Phys. Core 6, 063 (2023) · published 15 September 2023 | · pdf

In this work, multipartite entanglement is classified by polynomials. I show that the operator size is closely related to the entanglement structure. Given a generic quantum state, I define a series of subspaces generated by operators of different sizes acting on it. The information about the entanglement is encoded into these subspaces. With the dimension of these subspaces as coefficients, I define a polynomial which I call the entanglement polynomial. The entanglement polynomial induces a homomorphism from quantum states to polynomials. It implies that we can characterize and find the building blocks of entanglement by polynomial factorization. Two states share the same entanglement polynomial if they are equivalent under the stochastic local operations and classical communication. To calculate the entanglement polynomial practically, I construct a series of states, called renormalized states, whose ranks are related to the coefficients of the entanglement polynomial.
A note on the Noether-Wald and generalized Komar charges

Tomás Ortín, Matteo Zatti

SciPost Phys. Core 8, 094 (2025) · published 22 December 2025 | · pdf

We propose a simple algorithm to compute the generalized Komar charge of any exactly gauge- and diffeomorphism-invariant theory.
Search for anomalous quartic gauge couplings in the process $\mu^+\mu^-\to \bar{\nu}\nu\gamma\gamma$ with a nested local outlier factor

Ke-Xin Chen, Yu-Chen Guo, Ji-Chong Yang

SciPost Phys. Core 8, 091 (2025) · published 11 December 2025 | · pdf

In recent years, with the increasing luminosities of colliders, handling the growing amount of data has become a major challenge for future new physics (NP) phenomenological research. To improve efficiency, machine learning algorithms have been introduced into the field of high-energy physics. As a machine learning algorithm, the local outlier factor (LOF), and the nested LOF (NLOF) are potential tools for NP phenomenological studies. In this work, the possibility of searching for the signals of anomalous quartic gauge couplings (aQGCs) at muon colliders using the NLOF is investigated. Taking the process $\mu^+\mu^-\to \nu\bar{\nu}\gamma\gamma$ as an example, the signals of dimension-8 aQGCs are studied, expected coefficient constraints are presented. The event selection strategy uses unsupervised anomaly scores, with supervised optimization for EFT sensitivity. The NLOF algorithm is shown to outperform the k-means based anomaly detection methods, and a traditional counterpart.
Phase space compression of a positive muon beam in two spatial dimensions

A. Antognini, N. J. Ayres, I. Belosevic, V. Bondar, A. Eggenberger, M. Hildebrandt, R. Iwai, K. Kirch, A. Knecht, G. Lospalluto, J. Nuber, A. Papa, M. Sakurai, I. Solovyev, D. Taqqu, T. Yan

SciPost Phys. Core 8, 071 (2025) · published 20 October 2025 | · pdf

We present the first demonstration of simultaneous phase space compression in two spatial dimensions of a positive muon beam, the first stage of the novel high-brightness muon beam under development by the muCool collaboration at the Paul Scherrer Institute. The keV-energy, sub-mm size beam would enable a factor $10^5$ improvement in brightness for precision $\mu$SR, and atomic and particle physics measurements with positive muons. This compression is achieved within a cryogenic helium gas target with a strong density gradient, placed in a homogeneous magnetic field, under the influence of a complex electric field. In the next phase, the muon beam will be extracted into vacuum.
Ground state analysis of the spin-1/2 XX chain model with anisotropic three-spin interaction

Nima Mahboob, Saeed Mahdavifar, Fatemeh Khastehdel Fumani

SciPost Phys. Core 8, 050 (2025) · published 11 August 2025 | · pdf

In this paper, we investigate the ground state properties of the spin-1/2 XX chain model with anisotropic three-spin interaction using the fermionization technique. By exactly diagonalizing the Hamiltonian, we analyze the dispersion relation, ground state energy, and order parameters. Our findings identify two gapless phases, distinguished by a Lifshitz transition line: one exhibiting long-range chiral correlations and the other characterized by chiral-nematic correlations. These correlations do not correspond to conventional symmetry-breaking local order parameters typically associated with gapped one-dimensional phases but instead signify emergent quantum coherence in the gapless regime. Further, we study the ground state phase diagram through the concurrence and quantum discord between nearest-neighbor spins, finding that these measures are maximized at the critical line, with an additional entangled region observed. Finally, we examine the spin squeezing parameter and entanglement entropy, demonstrating that the ground state is squeezed throughout and becomes extremely squeezed at the critical line. Notably, in the gapless chiral-nematic phase, the Heisenberg limit is achieved. By dividing the system into two equal parts, we observe significant entanglement in the gapless chiral phase. The central charge calculation confirms the critical nature of the gapless chiral-nematic phase, while the entanglement entropy follows volume-law scaling in the gapless chiral phase.
Quantifying the effects of noise in a quantum convolutional neural network

Zeyu Fan, Jonathan Wei Zhong Lau, Leong-Chuan Kwek

SciPost Phys. Core 8, 093 (2025) · published 18 December 2025 | · pdf

This study quantifies the effects of quantum noise on the performance of a quantum convolutional neural network (QCNN), building on parallels with classical convolutional neural networks (CNNs), where added Gaussian noise can improve training speed, accuracy, and generalizability. While such benefits are established for classical CNNs, the influence of noise on quantum counterparts remains insufficiently characterized. We specifically examine three types of quantum noise: decoherence, Gaussian noise arising from imperfect quantum gates and experimental error, and systematic noise introduced during input state preparation. Our analysis provides a detailed assessment of how these distinct noise sources affect QCNN operation and outlines considerations for mitigating their impact. Though a QCNN is used as an example in this work, the methods used here can be applied to other quantum machine learning models as well.
A field theory representation of sum of powers of principal minors and physical applications

Morteza Nattagh Najafi, Abolfazl Ramezanpour, Mohammad Ali Rajabpour

SciPost Phys. Core 8, 051 (2025) · published 12 August 2025 | · pdf

We introduce a novel field theory representation for the Sum of Powers of Principal Minors (SPPM), a mathematical construct with profound implications in quantum mechanics and statistical physics. We begin by establishing a Berezin integral formulation of the SPPM problem, showcasing its versatility through various symmetries including $SU(n)$, its subgroups, and particle-hole symmetry. This representation not only facilitates new analytical approaches but also offers deeper insights into the symmetries of complex quantum systems. For instance, it enables the representation of the Hubbard model's partition function in terms of the SPPM problem. We further develop three mean field techniques to approximate SPPM, each providing unique perspectives and utilities: the first method focuses on the evolution of symmetries post-mean field approximation, the second, based on the bosonic representation, enhances our understanding of the stability of mean field results, and the third employs a variational approach to establish a lower bound for SPPM. These methods converge to identical consistency relations and values for SPPM, illustrating their robustness. The practical applications of our theoretical advancements are demonstrated through two compelling case studies. First, we exactly solve the SPPM problem for the Laplacian matrix of a chain, a symmetric tridiagonal matrix, allowing for precise benchmarking of mean-field theory results. Second, we present the first analytical calculation of the Shannon-Rényi entropy for the transverse field Ising chain, revealing critical insights into phase transitions and symmetry breaking in the ferromagnetic phase. This work not only bridges theoretical gaps in understanding principal minors within quantum systems but also sets the stage for future explorations in more complex quantum and statistical physics models.

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