Publications

Order by: publication date number of citations

• 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 | Toggle abstract · 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 $\xi \ll L \ll (\xi/\pi^2) \ln^2(\Delta_\xi/\Delta)$.

• Fusion of irreducible modules in the periodic Temperley–Lieb algebra

  Yacine Ikhlef, Alexi Morin-Duchesne

  SciPost Phys. 17, 132 (2024) · published 12 November 2024 | Toggle abstract · pdf

  We propose a new family $\mathsf{Y}_{k,\ell,x,y,[z,w]}$ of modules over the enlarged periodic Temperley–Lieb algebra $\mathsf{\mathcal EPTL}_N(\beta)$. These modules are built from link states with two marked points, similarly to the modules $\mathsf{X}_{k,\ell,x,y,z}$ that we constructed in a previous paper. They however differ in the way that defects connect pairwise. We analyse the decomposition of $\mathsf{Y}_{k,\ell,x,y,[z,w]}$ over the irreducible standard modules $\mathsf{W}_{k,x}$ for generic values of the parameters $z$ and $w$, and use it to deduce the fusion rules for the fusion $\mathsf{W} × \mathsf{W}$ of standard modules. These turn out to be more symmetric than those obtained previously using the modules $\mathsf{X}_{k,\ell,x,y,z}$. From the work of Graham and Lehrer, it is known that, for $\beta = -q-q^{-1}$ where $q$ is not a root of unity, there exists a set of non-generic values of the twist $y$ for which the standard module $\mathsf{W}_{\ell,y}$ is indecomposable yet reducible with two composition factors: a radical submodule $\mathsf{R}_{\ell,y}$ and a quotient module $\mathsf{Q}_{\ell,y}$. Here, we construct the fusion products $\mathsf{W}×\mathsf{R}$, $\mathsf{W}×\mathsf{Q}$ and $\mathsf{Q} × \mathsf{Q}$, and analyse their decomposition over indecomposable modules. For the fusions involving the quotient modules $\mathsf{Q}$, we find very simple results reminiscent of $\mathfrak{sl}(2)$ fusion rules. This construction with modules $\mathsf{Y}_{k,\ell,x,y,[z,w]}$ is a good lattice regularization of the operator product expansion in the underlying logarithmic bulk conformal field theory. Indeed, it fits with the correspondence between standard modules and connectivity operators, and is useful for the calculation of their correlation functions. Remarkably, we show that the fusion rules $\mathsf{W}×\mathsf{Q}$ and $\mathsf{Q}×\mathsf{Q}$ are consistent with the known fusion rules of degenerate primary fields.

• 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 | Toggle abstract · 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.

• Exact effective action for the O(N) vector model in the large N limit

  Han Ma, Sung-Sik Lee

  SciPost Phys. 15, 111 (2023) · published 22 September 2023 | Toggle abstract · pdf

  We present the Wilsonian effective action as a solution of the exact RG equation for the critical $O(N)$ vector model in the large $N$ limit. Below four dimensions, the exact effective action can be expressed in a closed form as a transcendental function of two leading scaling operators with infinitely many derivatives. From the exact solution that describes the RG flow from a UV theory to the fixed point theory in the IR, we obtain the mapping between UV operators and IR scaling operators. It is shown that IR scaling operators are given by sums of infinitely many UV operators with infinitely many derivatives.

• Bootstrapping nonequilibrium stochastic processes

  Minjae Cho

  SciPost Phys. 19, 124 (2025) · published 10 November 2025 | Toggle abstract · pdf

  We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate linear programming problems that use positivity and invariance property of invariant measures to derive rigorous bounds on their expectation values. Second, for time evolution in asynchronous processes, we exploit the master equation along with positivity and initial conditions to construct linear and semidefinite programming problems that yield bounds on expectation values at both short and late times. We illustrate both approaches using two canonical examples: the contact process in 1+1 and 2+1 dimensions, and the Domany-Kinzel model in both synchronous and asynchronous forms in 1+1 dimensions. Our bounds on invariant measures yield rigorous lower bounds on critical rates, while those on time evolutions provide two-sided bounds on the half-life of the infection density and the temporal correlation length in the subcritical phase.

• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories

  Usman Naseer, Charles Thull

  SciPost Phys. 13, 058 (2022) · published 21 September 2022 | Toggle abstract · pdf

  We study $\mathcal{N}=2$ theories on four-dimensional manifolds that admit a Killing vector $v$ with isolated fixed points. It is possible to deform these theories by coupling position-dependent background fields to the flavor current multiplet. The partition function of the deformed theory only depends on the value of the background scalar fields at the fixed points of $v$. For a single adjoint hypermultiplet, the partition function becomes independent of the supergravity as well as the flavor background if the scalars attain special values at the fixed points. For these special values, supersymmetry at the fixed points enhances from the Donaldson-Witten twist to the Marcus twist or the Vafa-Witten twist of $\mathcal{N}=4$ SYM. Our results explain the recently observed squashing independence of $\mathcal{N}=2^*$ theory on the squashed sphere and provide a new squashing independent point. Interpreted through the AGT-correspondence, this implies the $b$-independence of torus one-point functions of certain local operators in Liouville/Toda CFT. The position-dependent deformations imply relations between correlators of partially integrated operators in any $\mathcal{N}=2$ SCFT with flavor symmetries.

• Logarithmic operators in $c=0$ bulk CFTs

  Yifei He

  SciPost Phys. 19, 008 (2025) · published 4 July 2025 | Toggle abstract · pdf

  We study Kac operators (e.g. energy operator) in percolation and self-avoiding walk bulk CFTs with central charge $c=0$. The proper normalizations of these operators can be deduced at generic $c$ by requiring the finiteness and reality of the three-point constants in cluster and loop model CFTs. At $c=0$, Kac operators become zero-norm states and the bottom fields of logarithmic multiplets, and comparison with $c<1$ Liouville CFT suggests the potential existence of arbitrarily high rank Jordan blocks. We give a generic construction of logarithmic operators based on Kac operators and focus on the rank-2 pair of the energy operator mixing with the hull operator. By taking the $c\to 0$ limit, we compute some of their conformal data and use this to investigate the operator algebra at $c=0$. Based on cluster decomposition, we find that, contrary to previous belief, the four-point correlation function of the bulk energy operator does not vanish at $c=0$, and a crucial role is played by its coupling to the rank-3 Jordan block associated with the second energy operator. This reveals the intriguing way zero-norm operators build long-range higher-point correlations through the intricate logarithmic structures in $c=0$ bulk CFTs.

• Dynamic hysteresis across a dissipative multi-mode phase transition

  Marvin Röhrle, Jens Benary, Erik Bernhart, Herwig Ott

  SciPost Phys. 16, 158 (2024) · published 28 June 2024 | Toggle abstract · pdf

  Dissipative phase transitions are characteristic features in open quantum systems. Key signatures are the dynamical switching between different states in the vicinity of the phase transition and the appearance of hysteresis. Here, we experimentally study dynamic sweeps across a first order dissipative phase transition in a multi-mode driven-dissipative system. In contrast to previous studies, we perform sweeps of the dissipation strength instead of the driving strength. We extract exponents for the scaling of the hysteresis area in dependence of the sweep time and study the $g^{(2)}(0)$ correlations, which show non-trivial behavior. By changing the temperature of the system we investigate the importance of coherently pumping the system. We compare our results to numerical calculations done for a single mode variant of the system, and find surprisingly good agreement. Furthermore, we identify and discuss the differences between a scan of the dissipation strength and a scan of the driving strength.

• Bethe vectors and recurrence relations for twisted Yangian based models

  Vidas Regelskis

  SciPost Phys. 17, 126 (2024) · published 5 November 2024 | Toggle abstract · pdf

  We study Olshanski twisted Yangian based models, known as one-dimensional "soliton non-preserving" open spin chains, by means of algebraic Bethe Ansatz. The even case, when the bulk symmetry is $\mathfrak{gl}_{2n}$ and the boundary symmetry is $\mathfrak{sp}_{2n}$ or $\mathfrak{so}_{2n}$, was studied in [Ann. Henri Poincaré 20, 339 (2018)]. In the present work, we focus on the odd case, when the bulk symmetry is $\mathfrak{gl}_{2n+1}$ and the boundary symmetry is $\mathfrak{so}_{2n+1}$. We explicitly construct Bethe vectors and present a more symmetric form of the trace formula. We use the composite model approach and $Y(\mathfrak{gl}_n)$-type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.

• Emergent dipole field theory in atomic ladders

  Hernan B. Xavier, Poetri Sonya Tarabunga, Marcello Dalmonte, Rodrigo G. Pereira

  SciPost Phys. 18, 184 (2025) · published 10 June 2025 | Toggle abstract · pdf

  We study the dynamics of hard-core bosons on ladders, in the presence of strong kinetic constrains akin to those of the Bariev model. We use a combination of analytical methods and numerical simulations to establish the phase diagram of the model. The model displays a paired Tomonaga-Luttinger liquid phase featuring an emergent dipole symmetry, which encodes the local pairing constraint into a global, nonlocal quantity. We scrutinize the effect of such emergent low-energy symmetry during quench dynamics including single-particle defects. We observe that, despite being approximate, the dipole symmetry still leads to very slow relaxation dynamics, which we model via an effective field theory. The model we discuss is amenable to realization in both cold atoms in optical lattices and Rydberg atom arrays with dynamics taking place solely in the Rydberg manifold. To observe the unusual dynamics of excitations in such experimental platforms, we propose a two-step protocol, which starts with the quasi-adiabatic preparation of low-energy states, followed by the local creation of defects and their study under quench dynamics.