Publications

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Chaos enhancement in large-spin chains

Yael Lebel, Lea F. Santos, Yevgeny Bar Lev

SciPost Phys. 15, 022 (2023) · published 21 July 2023 | · pdf

We study the chaotic properties of a large-spin XXZ chain with onsite disorder and a small number of excitations above the fully polarized state. We show that while the classical limit, which is reached for large spins, is chaotic, enlarging the spin suppresses quantum chaos features. We examine ways to facilitate chaos by introducing additional terms to the Hamiltonian. Interestingly, perturbations that are diagonal in the basis of product states in the $z$-direction do not lead to significant enhancement of chaos, while off-diagonal perturbations restore chaoticity for large spins, so that only three excitations are required to achieve strong level repulsion and ergodic eigenstates.
Efficient higher-order matrix product operators for time evolution

Maarten Van Damme, Jutho Haegeman, Ian McCulloch, Laurens Vanderstraeten

SciPost Phys. 17, 135 (2024) · published 15 November 2024 | · pdf

We introduce a systematic construction of higher-order matrix product operator (MPO) approximations of the time evolution operator for generic (short and long range) one-dimensional Hamiltonians. We demonstrate the utility of our construction, by showing an order of magnitude speedup in simulation cost compared to conventional first-order MPO time evolution schemes.
Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group

Miriam Patricolo, Marcel Gievers, Kilian Fraboulet, Aiman Al-Eryani, Sarah Heinzelmann, Pietro M. Bonetti, Alessandro Toschi, Demetrio Vilardi, Sabine Andergassen

SciPost Phys. 18, 078 (2025) · published 4 March 2025 | · pdf

We extend the recently introduced single-boson exchange formulation to the computation of the self-energy from the Schwinger–Dyson equation (SDE). In particular, we derive its expression both in diagrammatic and in physical channels. The simple form of the single-boson exchange SDE, involving only the bosonic propagator and the fermion-boson vertex, but not the rest function, allows for an efficient numerical implementation. We furthermore discuss its implications in a truncated unity solver, where a restricted number of form factors introduces an information loss in the projection of the momentum dependence that in general affects the equivalence between the different channel representations. In the application to the functional renormalization group, we find that the convergence in the number of form factors depends on the channel representation of the SDE. For the two-dimensional Hubbard model at weak coupling, the pseudogap opening driven by antiferromagnetic fluctuations is captured already by a single ($s$-wave) form factor in the magnetic channel representation, differently to the density and superconducting channels.
Refined cyclic renormalization group in Russian doll model

Vedant Motamarri, Ivan M. Khaymovich, Alexander Gorsky

SciPost Phys. 17, 157 (2024) · published 6 December 2024 | · pdf

Focusing on Bethe-Ansatz integrable models, robust to both time-reversal symmetry breaking and disorder, we consider the Russian Doll Model (RDM) for finite system sizes and energy levels. Suggested as a time-reversal-symmetry breaking deformation of Richardson's model, the well-known and simplest model of superconductivity, RDM revealed an unusual cyclic renormalization group (RG) over the system size $N$, where the energy levels repeat themselves, shifted by one after a finite period in $\ln N$, supplemented by a hierarchy of superconducting condensates, with the superconducting gaps following the so-called Efimov (exponential) scaling. The equidistant single-particle spectrum of RDM made the above Efimov scaling and cyclic RG to be asymptotically exact in the wideband limit of the diagonal potential. Here, we generalize this observation in various respects. We find that, beyond the wideband limit, when the entire spectrum is considered, the periodicity of the spectrum is not constant, but appears to be energy-dependent. Moreover, we resolve the apparent paradox of shift in the spectrum by a single level after the RG period, despite the disappearance of a finite fraction of energy levels. We also analyze the effects of disorder in the diagonal potential on the above periodicity and show that it survives only for high energies beyond the energy interval of the disorder amplitude. Our analytic analysis is supported with exact diagonalization.
BPS chaos

Yiming Chen, Henry W. Lin, Stephen H. Shenker

SciPost Phys. 18, 072 (2025) · published 27 February 2025 | · pdf

Black holes are chaotic quantum systems that are expected to exhibit random matrix statistics in their finite energy spectrum. Lin, Maldacena, Rozenberg and Shan (LMRS) have proposed a related characterization of chaos for the ground states of BPS black holes with finite area horizons. On a separate front, the "fuzzball program" has uncovered large families of horizon-free geometries that account for the entropy of holographic BPS systems, but only in situations with sufficient supersymmetry to exclude finite area horizons. The highly structured, non-random nature of these solutions seems in tension with strong chaos. We verify this intuition by performing analytic and numerical calculations of the LMRS diagnostic in the corresponding boundary quantum system. In particular we examine the 1/2 and 1/4-BPS sectors of $\mathcal{N}=4$ SYM, and the two charge sector of the D1-D5 CFT. We find evidence that these systems are only weakly chaotic, with a Thouless time determining the onset of chaos that grows as a power of $N$. In contrast, finite horizon area BPS black holes should be strongly chaotic, with a Thouless time of order one. In this case, finite energy chaotic states become BPS as $N$ is decreased through the recently discovered "fortuity" mechanism. Hence they can plausibly retain their strongly chaotic character.
Resonating valence bonds and spinon pairing in the Dicke model

R. Ganesh, L. Theerthagiri, G. Baskaran

SciPost Phys. 4, 044 (2018) · published 30 June 2018 | · pdf

Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms (with states $\vert 0 \rangle$ and $\vert 1 \rangle$) coupled to a common photon mode. In the lossy cavity limit, starting with an initial state of $M$ atoms excited and $N$ atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets of the form $\frac{1}{\sqrt{2}}[\vert 0 1 \rangle - \vert 1 0 \rangle]$. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or `spinons'. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to a mixed quantum state with a fluctuating number of spinon pairs -- an inchoate superconductor. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization ($M-N$), the emission exhibits a continuous transition from a dark state to a bright state. This is reflected in the spinon pair number distribution which can be tuned from sub-poissonian to super-poissonian regimes. This opens an exciting route to simulate RVB states and superconductivity.
Modelling the underlying event in photon-initiated processes

Jonathan Butterworth, Ilkka Helenius, Juan Jose Juan Castella, Bradley Pattengale, Shahzad Sanjrani, Matthew Wing

SciPost Phys. 17, 158 (2024) · published 9 December 2024 | · pdf

Modelling the underlying event in high-energy hadronic collisions is important for physics at colliders. This includes lepton colliders, where low-virtuality photons accompanying the lepton beam(s) may develop hadronic structure. Similarly, photon-induced collisions also occur in proton or heavy-ion beam experiments. While the underlying event in proton-proton collisions has been the subject of much study at the LHC, studies of hadronic-photon-induced underlying event are now of increasing interest in light of planned future lepton and lepton-hadron colliders, as well as the photon-induced processes in ultra-peripheral collisions at the LHC. Here we present an investigation of the underlying event in photon-initiated processes, starting from the Pythia models used to describe LHC and Tevatron data, and revisiting HERA and LEP2 data. While no single tune describes all the data with different beam configurations, we find that a good agreement can still be found within the same model by adjusting the relevant parameters separately for $\gamma\gamma$, $\gamma p$ and $pp$. This suggests that the basic model of multiparton interaction implemented in Pythia can be applied for different beam configurations. Furthermore, we find that a reasonable agreement for $\gamma\gamma$ and $\gamma p$ data, and for $pp$ data at an LHC reference energy, can be found within a single parametrization, but $pp$ collisions would prefer a stronger energy dependence, leading to too many multiparton interactions in lower energy photon-induced collisions. On this basis, we make some recommendations for simulations of photon-induced processes, such as $\gamma \gamma$ events at the LHC or FCC and $ep$ or $eA$ collisions at the EIC, and suggest possibilities for improvements in the modelling.
Pairing symmetry and fermion projective symmetry groups

Xu Yang, Sayak Biswas, Shuangyuan Lu, Mohit Randeria, Yuan-Ming Lu

SciPost Phys. 17, 161 (2024) · published 10 December 2024 | · pdf

The Ginzburg-Landau (GL) theory is very successful in describing the pairing symmetry, a fundamental characterization of the broken symmetries in a paired superfluid or superconductor. However, GL theory does not describe fermionic excitations such as Bogoliubov quasiparticles or Andreev bound states that are directly related to topological properties of the superconductor. In this work, we show that the symmetries of the fermionic excitations are captured by a Projective Symmetry Group (PSG), which is a group extension of the bosonic symmetry group in the superconducting state. We further establish a correspondence between the pairing symmetry and the fermion PSG. When the normal and superconducting states share the same spin rotational symmetry, there is a simpler correspondence between the pairing symmetry and the fermion PSG, which we enumerate for all 32 crystalline point groups. We also discuss the general framework for computing PSGs when the spin rotational symmetry is spontaneously broken in the superconducting state. This PSG formalism leads to experimental consequences, and as an example, we show how a given pairing symmetry dictates the classification of topological superconductivity.
Growth of the Wang-Casati-Prosen counter in an integrable billiard

Zaijong Hwang, Christoph A. Marx, Joseph J. Seaward, Svetlana Jitomirskaya, Maxim Olshanii

SciPost Phys. 14, 017 (2023) · published 10 February 2023 | · pdf

This work is motivated by an article by Wang, Casati, and Prosen [Phys. Rev. E vol. 89, 042918 (2014)] devoted to a study of ergodicity in two-dimensional irrational right-triangular billiards. Numerical results presented there suggest that these billiards are generally not ergodic. However, they become ergodic when the billiard angle is equal to $\pi/2$ times a Liouvillian irrational, morally a class of irrational numbers which are well approximated by rationals. In particular, Wang et al. study a special integer counter that reflects the irrational contribution to the velocity orientation; they conjecture that this counter is localized in the generic case, but grows in the Liouvillian case. We propose a generalization of the Wang-Casati-Prosen counter: this generalization allows to include rational billiards into consideration. We show that in the case of a $45°\!\!:\!45°\!\!:\!90°$ billiard, the counter grows indefinitely, consistent with the Liouvillian scenario suggested by Wang et al.
Universal performance gap of neural quantum states applied to the Hofstadter-Bose-Hubbard model

Eimantas Ledinauskas, Egidijus Anisimovas

SciPost Phys. 18, 011 (2025) · published 10 January 2025 | · pdf

Neural Quantum States (NQS) have demonstrated significant potential in approximating ground states of many-body quantum systems, though their performance can be inconsistent across different models. This study investigates the performance of NQS in approximating the ground state of the Hofstadter-Bose-Hubbard (HBH) model, an interacting boson system on a two-dimensional square lattice with a perpendicular magnetic field. Our results indicate that increasing magnetic flux leads to a substantial increase in energy error, up to three orders of magnitude. Importantly, this decline in NQS performance is consistent across different optimization methods, neural network architectures, and physical model parameters, suggesting a significant challenge intrinsic to the model. Despite investigating potential causes such as wave function phase structure, quantum entanglement, fractional quantum Hall effect, and the variational loss landscape, the precise reasons for this degradation remain elusive. The HBH model thus proves to be an effective testing ground for exploring the capabilities and limitations of NQS. Our study highlights the need for advanced theoretical frameworks to better understand the expressive power of NQS which would allow a systematic development of methods that could potentially overcome these challenges.

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