Publications

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Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations

Kohtaroh Sakaue, Hiroshi Shinaoka, Rihito Sakurai

SciPost Phys. 19, 038 (2025) · published 14 August 2025 | · pdf

Tensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT is more advantageous than interpolating the noise. Here, we propose a new method that starts with an initial guess of TT and optimizes it using non-linear least-squares by fitting it to measured points obtained from TCI. We use quantics TCI (QTCI) in this method and demonstrate its effectiveness on sine and two-time correlation functions, with each evaluated with random noise. The resulting QTT exhibits increased robustness against noise compared to the QTCI method. Furthermore, we employ this optimized QTT of the correlation function in quantum simulation based on pseudo-imaginary-time evolution, resulting in ground-state energy with higher accuracy than the QTCI or Monte Carlo methods.
On the breakdown of dimensional reduction and supersymmetry in random-field models

Gilles Tarjus, Matthieu Tissier, Ivan Balog

SciPost Phys. 19, 001 (2025) · published 1 July 2025 | · pdf

We discuss the breakdown of the Parisi-Sourlas supersymmetry (SUSY) and of the dimensional-reduction (DR) property in the random field Ising and O($N$) models as a function of space dimension $d$ and/or number of components $N$. The functional renormalization group (FRG) predicts that this takes place below a critical line $d_\mathrm{DR}(N)$. We revisit the perturbative FRG results for the RFO($N$)M in $d=4+\epsilon$ and carry out a more comprehensive investigation of the nonperturbative FRG approximation for the RFIM. In light of this FRG description, we discuss the perturbative results in $\epsilon=6-d$ recently derived for the RFIM by Kaviraj, Rychkov, and Trevisani. We stress in particular that the disappearance of the SUSY/DR fixed point below $d_\mathrm{DR}$ arises as a consequence of the nonlinearity of the FRG equations and cannot be found via the perturbative expansion in $\epsilon=6-d$ (nor in $1/N$). We also provide an error bar on the value of the critical dimension $d_\mathrm{DR}$ for the RFIM, which we find around $5.11±0.09$, by studying several successive orders of the nonperturbative FRG approximation scheme.
Dualities between 2+1d fusion surface models from braided fusion categories

Luisa Eck

SciPost Phys. 19, 157 (2025) · published 17 December 2025 | · pdf

Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} ≠ \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones.
The asymmetric Fermi surface of Bi2201

Steef Smit, Kourosh L. Shirkoohi, Saumya Mukherjee, Sergio Barquero Pierantoni, Lewis Bawden, Erik van Heumen, Arnaud P. N. Tchiomo, Jans Henke, Jasper van Wezel, Yingkai Huang, Takeshi Kondo, Tsunehiro Takeuchi, Timur K. Kim, Cephise Cacho, Marta Zonno, Sergey Gorovikov, Stephen B. Dugdale, Jorge I. Facio, Mariia Roslova, Laura Folkers, Anna Isaeva, Nigel E. Hussey, Mark S. Golden

SciPost Phys. 18, 191 (2025) · published 17 June 2025 | · pdf

High-resolution angle-resolved photoemission spectroscopy (ARPES) performed on the single-layered cuprate (Pb$_{1-y}$,Bi$_y$)$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (Bi2201) reveals a 6-10% difference in the nodal $k_F$ vectors along the $\Gamma$Y and $\Gamma$X directions. This asymmetry is notably larger than the 2% orthorhombic distortion in the CuO$_2$ plane lattice constants determined using X-ray crystallography from the same samples. First principles calculations indicate that crystal-field splitting of the bands lies at the root of the $k_{F}$ asymmetry. Concomitantly, the nodal Fermi velocities for the $\Gamma$Y quadrant exceed those for $\Gamma$X by 4%. Momentum distribution curve widths for the two nodal dispersions are also anisotropic, showing identical energy dependencies, bar a scaling factor of $\sim$ 1.17$± 0.05$ between $\Gamma$Y and $\Gamma$X. Consequently, the imaginary part of the self-energy is found to be 10-20% greater along $\Gamma$Y than $\Gamma$X. These results emphasize the need to account for Fermi surface asymmetry in the analysis of ARPES data on Bi-based cuprate high temperature superconductors such as Bi2201. To illustrate this point, an orthorhombic tight-binding model (with twofold in-plane symmetry) was used to fit ARPES Fermi surface maps spanning all four quadrants of the Brillouin zone, and the ARPES-derived hole-doping (Luttinger count) was extracted. Comparison of the Luttinger count with one assuming four-fold in-plane symmetry strongly suggests the marked spread in previously-reported Fermi surface areas from ARPES on Bi2201 results from the differences in $k_F$ along $\Gamma$Y and $\Gamma$X. Using this analysis, a new, linear relationship emerges between the hole-doping derived from ARPES ($p_{\text{ARPES}}$) and that derived using the Presland ($p_{\text{Presland}}$) relation such that $p_{\text{ARPES}} = p_{\text{Presland}}+0.11$. The implications for this difference between the ARPES- and Presland-derived estimates for $p$ are discussed and possible future directions to elucidate the origin of this discrepancy are presented.
Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases

Maciej Łebek, Miłosz Panfil

SciPost Phys. 18, 186 (2025) · published 12 June 2025 | · pdf

Integrable systems feature an infinite number of conserved charges and on hydrodynamic scales are described by generalised hydrodynamics (GHD). This description breaks down when the integrability is weakly broken and sufficiently large space-time-scales are probed. The emergent hydrodynamics depends then on the charges conserved by the perturbation. We focus on nearly-integrable Galilean-invariant systems with conserved particle number, momentum and energy. Basing on the Boltzmann approach to integrability-breaking we describe dynamics of the system with GHD equation supplemented with a collision term. The limit of large space-time-scales is addressed using Chapman-Enskog expansion adapted to the GHD equation. For length scales larger than $\sim \lambda^{-2}$, where $\lambda$ is integrability-breaking parameter, we recover Navier-Stokes equations and find transport coefficients: viscosity and thermal conductivity. At even larger length scales, this description crosses over to Kardar-Parisi-Zhang universality class, characteristic to generic non-integrable one-dimensional fluids. Employing nonlinear fluctuating hydrodynamics we estimate this crossover length scale as $ \sim \lambda^{-4}$.
Fusion of low-entanglement excitations in 2D toric code

Jing-Yu Zhao, Xie Chen

SciPost Phys. 18, 106 (2025) · published 20 March 2025 | · pdf

On top of a $D$-dimensional gapped bulk state, Low Entanglement Excitations (LEE) on $d(<D)$-dimensional sub-manifolds can have extensive energy but preserves the entanglement area law of the ground state. Due to their multi-dimensional nature, the LEEs embody a higher-category structure in quantum systems. They are the ground state of a modified Hamiltonian and hence capture the notions of 'defects' of generalized symmetries. In previous works, we studied the low-entanglement excitations in a trivial phase as well as those in invertible phases. We find that LEEs in these phases have the same structure as lower-dimensional gapped phases and their defects within. In this paper, we study the LEEs inside non-invertible topological phases. We focus on the simple example of $\mathbb{Z}_2$ toric code and discuss how the fusion result of 1d LEEs with 0d morphisms can depend on both the choice of fusion circuit and the ordering of the fused defects.
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 | · 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.
Sparsity in the numerical six-point bootstrap

Sebastian Harris

SciPost Phys. 19, 151 (2025) · published 10 December 2025 | · pdf

The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a six-point generalisation of the numerical bootstrap, yielding qualitatively new, rigorous bounds on CFT data. However, the numerical six-point bootstrap requires solving SDPs involving infinite-dimensional matrices, which has so far limited its applicability and hindered scalability in early implementations. This work overcomes the challenges by using sparse matrix decompositions to exploit the banded structure of the underlying SDP. The result is a rewriting of one-dimensional six-point bootstrap problems as effectively two-dimensional standard mixed correlator four-point bootstrap computations. As application, novel bounds whose extremal correlators interpolate between the six-point functions of the generalised free fermion and boson are derived. The extremal interpolations are matched with perturbative deformations of the massive free boson in AdS$_2$.
Learning the non-Markovian features of subsystem dynamics

Michele Coppola, Mari Carmen Bañuls, Zala Lenarčič

SciPost Phys. 19, 149 (2025) · published 8 December 2025 | · pdf

The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.
Quantum scars and caustics in Majorana billiards

R. Johanna Zijderveld, A. Mert Bozkurt, Michael Wimmer, İnanç Adagideli

SciPost Phys. 17, 147 (2024) · published 28 November 2024 | · pdf

We demonstrate that the classical dynamics influence the localization behaviour of Majorana wavefunctions in Majorana billiards. By using a connection between Majorana wavefunctions and eigenfunctions of a normal state Hamiltonian, we show that Majorana wavefunctions in both p-wave and s-wave topological superconductors inherit the properties of the underlying normal state eigenfunctions. As an example, we demonstrate that Majorana wavefunctions in topological superconductors with chaotic shapes feature quantum scarring. Furthermore, we show a way to manipulate a localized Majorana wavefunction by altering the underlying classical dynamics using a local potential away from the localization region. Finally, in the presence of chiral symmetry breaking, we find that the Majorana wavefunction in convex-shaped Majorana billiards exhibits caustics formation, reminiscent of a normal state system with magnetic field.

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