Publications

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Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation

B. Pahlevanzadeh, P. Sahebsara, D. Sénéchal

SciPost Phys. 13, 040 (2022) · published 30 August 2022 | · pdf

We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek, relevant to a twist angle of $1.30^\circ$, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion $U$ is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.

2 citations
Constraints on physical computers in holographic spacetimes

Aleksander M. Kubicki, Alex May, David Pérez-Garcia

SciPost Phys. 16, 024 (2024) · published 23 January 2024 | · pdf

Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

2 citations
On the R-matrix realization of quantum loop algebras

A. Liashyk, S. Z. Pakuliak

SciPost Phys. 12, 146 (2022) · published 4 May 2022 | · pdf

We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\widehat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$, $D^{(1)}_n$, $A^{(2)}_{N-1}$. For each $U_q(\tilde{\mathfrak{g}})$ we investigate the commutation relations between Gauss coordinates of the fundamental $\mathbb{L}$-operators using embedding of the smaller algebra into bigger one. The new realization of these algebras in terms of the currents is given. The relations between all off-diagonal Gauss coordinates and certain projections from the ordered products of the currents are presented. These relations are important in applications to the quantum integrable models.

2 citations
Tensor network study of the Shastry-Sutherland model with weak interlayer coupling

Patrick C. G. Vlaar, Philippe Corboz

SciPost Phys. 15, 126 (2023) · published 2 October 2023 | · pdf

The layered material SrCu$_2$(BO$_3$)$_2$ has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu$_2$(BO$_3$)$_2$ under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around $J''/J\sim0.04-0.05$ than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu$_2$(BO$_3$)$_2$ to be around $J''/J\sim 0.027$ at ambient pressure.

2 citations
Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model

Veniamin A. Abalmasov

SciPost Phys. 16, 151 (2024) · published 6 June 2024 | · pdf

Free energy as a function of polarization is calculated for the square-lattice $J_1$-$J_2$ Ising model for $J_2 < |J_1|/2$ using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a metastable state with zero polarization in the ordered phase. In addition, the Landau free energy calculated within RLFA indicates a geometric slab-droplet phase transition at low temperature, which cannot be predicted by the mean field approximation. In turn, restricted free energy calculations for finite-size samples, exact and using MC simulations, reveal metastable states with a wide range of polarization values, but with only two domains. Taking into account the dependence of the restricted free energy on the nearest-neighbor correlations allows us to identify several more metastable states. The calculations also reveal additional slab-droplet transitions at $J_2 > |J_1|/4$. These findings enrich our knowledge of the $J_1$-$J_2$ Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.

2 citations
Generalised Gibbs Ensemble for spherically constrained harmonic models

Damien Barbier, Leticia F. Cugliandolo, Gustavo S. Lozano, Nicolás Nessi

SciPost Phys. 13, 048 (2022) · published 2 September 2022 | · pdf

We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on an $N$ dimensional sphere, and feels the effect of anisotropic harmonic potentials. We derive all relevant averaged static observables in the (thermodynamic) $N\rightarrow\infty$ limit. We compare them to their long-term dynamic averages finding excellent agreement in all phases of a non-trivial phase diagram determined by the characteristics of the initial conditions and the amount of energy injected or extracted in an instantaneous quench. We discuss the implications of our results for the proper Neumann model in which the spherical constraint is imposed strictly.

2 citations
Modified rational six vertex model on the rectangular lattice

Samuel Belliard, Rodrigo Alves Pimenta, Nikita A. Slavnov

SciPost Phys. 16, 009 (2024) · published 9 January 2024 | · pdf

We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified Izergin determinant. The proofs are based on the quantum inverse scattering method and its representation theory together with elementary linear algebra.

2 citations
Extremality as a consistency condition on subregion duality

Ronak M. Soni

SciPost Phys. 17, 133 (2024) · published 13 November 2024 | · pdf

In JT gravity coupled to a CFT, I argue without using the path integral that the entanglement wedge of a boundary region is bounded by a quantum extremal surface (QES). For any candidate not bounded by a QES, a unitary in the complement can make reconstruction within the candidate inconsistent with boundary causality. The case without islands is a direct consequence of subregion duality, and the case with islands can also be dealt with with a stronger assumption.

2 citations
Fidelity decay and error accumulation in random quantum circuits

Nadir Samos Sáenz de Buruaga, Rafał Bistroń, Marcin Rudziński, Rodrigo M. C. Pereira, Karol Życzkowski, Pedro Ribeiro

SciPost Phys. 19, 013 (2025) · published 8 July 2025 | · pdf

Fidelity decay captures the inevitable state degradation in any practical implementation of a quantum process. We devise bounds for the decay of fidelity for a generic evolution given by a random quantum circuit model that encompasses errors arising from the implementation of two-qubit gates and qubit permutations. We show that fidelity decays exponentially with both circuit depth and the number of qubits raised to an architecture-dependent power and we determine the decay rates as a function of the amplitude of the aforementioned errors. Furthermore, we demonstrate the utility of our results in benchmarking quantum processors using the quantum volume figure of merit and provide insights into strategies for improving processor performance. These findings pave the way for understanding how states evolving under generic quantum dynamics degrade due to the accumulation of different kinds of perturbations.

2 citations
Anisotropic Zeeman Splitting in YbNi4P2

Sara Karbassi, Saman Ghannadzadeh, Kristin Kliemt, Manuel Brando, Cornelius Krellner, Sven Friedemann

SciPost Phys. 5, 056 (2018) · published 30 November 2018 | · pdf

The electronic structure of heavy-fermion materials is highly renormalised at low temperatures with localised moments contributing to the electronic excitation spectrum via the Kondo effect. Thus, heavy-fermion materials are very susceptible to Lifshitz transitions due to the small effective Fermi energy arising on parts of the renormalised Fermi surface. Here, we study Lifshitz transitions that have been discovered in YbNi4P2 in high magnetic fields. We measure the angular dependence of the critical fields necessary to induce a number of Lifshitz transitions and find it to follow a simple Zeeman-shift model with anisotropic g-factor. This highlights the coherent nature of the heavy quasiparticles forming a renormalised Fermi surface. We extract information on the orientation of the Fermi surface parts giving rise to the Lifshitz transitions and we determine the anisotropy of the effective g-factor to be $\eta \approx 3.8$ in good agreement with the crystal field scheme of YbNi4P2.

2 citations

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