Publications

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Josephson effect in strongly disordered metallic wires

Mustafa E. Ismagambetov, Aleksey V. Lunkin, Pavel M. Ostrovsky

SciPost Phys. 19, 021 (2025) · published 17 July 2025 | · pdf

We study localization effects in Josephson junctions with two superconductors connected by a strongly disordered metallic wire of length $L$. The conventional description of the Josephson effect in such systems, based on the quasiclassical Usadel equation, neglects electron interference and is only applicable when $L$ is shorter than the localization length $\xi$ in the wire. We develop a more general theory for the Josephson effect using the non-linear sigma model that fully accounts for electron interference, and hence localization. We show that for $L \gg \xi$, three qualitatively different regimes of the Josephson current arise depending on the ratio of the superconducting order parameter $\Delta$ and the mean level spacing in the localization volume $\Delta_\xi$. We derive the average supercurrent as a function of the phase difference for all three regimes. Quite unexpectedly, we observe that the Ambegaokar-Baratoff relation between the average critical current and the normal-state conductance still holds in the strongly localized state when $\Delta_\xi \gg \Delta$ and $\xi \ll L \ll (\xi/\pi^2) \ln^2(\Delta_\xi/\Delta)$.
Skyrmion-vortex hybrid and spin wave solutions in ferromagnetic superconductors

Shantonu Mukherjee, Amitabha Lahiri

SciPost Phys. 19, 022 (2025) · published 18 July 2025 | · pdf

The coexistence of Ferromagnetism and superconductivity in so called ferromagnetic superconductors (FMSC) is an intriguing phenomenon which may lead to novel physical effects as well as applications. Here in this work we have explored the interplay of topological excitations, namely vortices and Skyrmions, in ferromagnetic superconductors using a field theoretic description of such systems. In particular, numerical solutions for the continuous spin field compatible to a given vortex profile are determined in absence and presence of a Dzyaloshinskii-Moriya interaction (DMI) term. The solutions show that the spin configuration is like a Skyrmion but intertwined with the vortex structure — the radius of the the Skyrmion-like solution depends on the penetration depth and also the polarity of the Skyrmion depends on the sign of the winding number. Thus our solution describes a Skyrmion-vortex composite — but as a topological object in a bulk ferromagnetic superconductor, rather than on the interface of a ferromagnet-superconductor heterostructure. We have also determined the spin wave solutions in such systems in presence and absence of a vortex. In absence of a vortex, the frequency and the wave vector satisfy a cubic equation which leads to various interesting features. In particular, we have shown that in the low frequency regime the minimum in dispersion relation shifts from $k=0$ to a non-zero $k$ value depending on the parameters. We also discuss the nature of spin wave dispersion when the frequency $\omega$ is close to the photon mass $\tilde{m}$\,, for which we find multiple local minima in the dispersion curve. The group velocity of the spin wave would change its sign across such a minimum which is unique to FMSC. Also, the spin wave modes around the local minimum looks like roton mode in superfluid and hence called a magnetic roton. In presence of a vortex, the spin wave amplitude is shown to vary spatially such that the profile looks like that of a Néel Skyrmion. Possible experimental signature of both solutions are also discussed.
Multi-orbital two-particle self-consistent approach – Strengths and limitations

Jonas B. Profe, Jiawei Yan, Karim Zantout, Philipp Werner, Roser Valentí

SciPost Phys. 19, 026 (2025) · published 21 July 2025 | · pdf

Extending many-body numerical techniques which are powerful in the context of simple model calculations to the realm of realistic material simulations can be a challenging task. Realistic systems often involve multiple active orbitals, which increases the complexity and numerical cost because of the large local Hilbert space and the large number of interaction terms or sign-changing off-diagonal Green's functions. The two-particle self-consistent approach (TPSC) is one such many-body numerical technique, for which multi-orbital extensions have proven to be involved due to the substantially more complex structure of the local interaction tensor. In this paper we extend earlier multi-orbital generalizations of TPSC by setting up two different variants of a fully self-consistent theory for TPSC in multi-orbital systems. We first investigate the strengths and limitations of the approach analytically and then benchmark both variants against dynamical mean-field theory (DMFT) and D-TRILEX results. We find that the exact behavior of the system can be faithfully reproduced in the weak-coupling regime, while at stronger couplings the performance of the two TPSC variants strongly depends on details of the system.
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.
Integrable fishnet circuits and Brownian solitons

Žiga Krajnik, Enej Ilievski, Tomaž Prosen, Benjamin J. A. Héry, Vincent Pasquier

SciPost Phys. 19, 027 (2025) · published 21 July 2025 | · pdf

We introduce classical many-body dynamics on a one-dimensional lattice comprising local two-body maps arranged on discrete space-time mesh that serve as discretizations of Hamiltonian dynamics with arbitrarily time-varying coupling constants. Time evolution is generated by passing an auxiliary degree of freedom along the lattice, resulting in a 'fishnet' circuit structure. We construct integrable circuits consisting of Yang-Baxter maps and demonstrate their general properties, using the Toda and anisotropic Landau-Lifschitz models as examples. Upon stochastically rescaling time, the dynamics is dominated by fluctuations and we observe solitons undergoing Brownian motion.
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.
Anti-holomorphic modes in vortex lattices

Brook J. Hocking, Thomas Machon

SciPost Phys. 14, 080 (2023) · published 24 April 2023 | · pdf

A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedure, secondly by taking the long-wavelength limit of Tkachenko's exact solution for a triangular vortex lattice. Solutions to the continuum theory are found, described by arbitrary anti-holomorphic functions, and give power-law localized edge modes. Numerical results for finite lattices show excellent agreement to the theory.
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.
Mechanical stability of resonant Bose-Fermi mixtures

Christian Gualerzi, Leonardo Pisani, Pierbiagio Pieri

SciPost Phys. 19, 039 (2025) · published 14 August 2025 | · pdf

We investigate the mechanical stability of Bose-Fermi mixtures at zero temperature in the presence of a tunable Feshbach resonance, which induces a competition between boson condensation and boson-fermion pairing when the boson density is smaller than the fermion density. Using a many-body diagrammatic approach validated by fixed-node Quantum Monte Carlo calculations and supported by recent experimental observations, we determine the minimal amount of boson-boson repulsion required to guarantee the stability of the mixture across the entire range of boson-fermion interactions from weak to strong coupling. Our stability phase diagrams indicate that mixtures with boson-to-fermion mass ratios near two, such as the $^{87}$Rb-$^{40}$K system, exhibit optimal stability conditions. Moreover, by applying our results to a recent experiment with a $^{23}$Na-$^{40}$K mixture, we find that the boson-boson repulsion was insufficient to ensure stability, suggesting that the experimental timescale was short enough to avoid mechanical collapse. On the other hand, we also show that even in the absence of boson-boson repulsion, Bose-Fermi mixtures become intrinsically stable beyond a certain coupling strength, preceding the quantum phase transition associated with the vanishing of the bosonic condensate. We thus propose an experimental protocol for observing this quantum phase transition in a mechanically stable configuration.
Z2 topological orders in kagome dipolar systems: Feedback from Rydberg quantum simulator

Pengwei Zhao, Gang v. Chen

SciPost Phys. 19, 040 (2025) · published 14 August 2025 | · pdf

The mutual feedback between quantum condensed matter and cold atom physics has been quite fruitful throughout history and continues to inspire ongoing research. Motivated by the recent activities on the quantum simulation of topological orders among the ultracold Rydberg atom arrays, we consider the possibility of searching for topological orders among the dipolar quantum magnets and polar molecules with a kagome lattice geometry. Together with other quantum interactions such as the transverse field, the dipolar interaction endows the kagome system with a similar structure as the Balents-Fisher-Girvin model and thus fosters the emergence of the $\mathbb{Z}_2$ topological orders. We construct a $\mathbb{Z}_2$ lattice gauge theory to access the topological ordered phase and describe the spinon and vison excitations for the $\mathbb{Z}_2$ topological orders. We explain the spectroscopic consequences for various quantum phases as well as the experimental detection. We further discuss the rare-earth kagome magnets, ultracold polar molecules, and cluster Mott insulators for the physical realization.

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