Publications

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Boundary chaos: Spectral form factor

Felix Fritzsch, Tomaž Prosen

SciPost Phys. 17, 142 (2024) · published 22 November 2024 | · pdf

Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed boundary chaos, in terms of the spectral form factor and its fluctuations. We exactly calculate the latter in the limit of large local Hilbert space dimension $q$ for different classes of random boundary interactions and find it to coincide with random matrix theory, possibly after a non-zero Thouless time. The latter effect is due to a drastic enhancement of the spectral form factor, when integer time and system size fulfill a resonance condition. We compare our semiclassical (large $q$) results with numerics at small local Hilbert space dimension ($q=2,3$) and observe qualitatively similar features as in the semiclassical regime.
Hole doping and electronic correlations in Cr substituted BaFe$_{2}$As$_{2}$

Marli dos Reis Cantarino, Kevin R. Pakuszewski, Bjoern Salzmann, Pedro H. A. Moya, Wagner R. da Silva Neto, Gabriel S. Freitas, Pascoal G. Pagliuso, Cris Adriano, Walber H. Brito, Fernando A. Garcia

SciPost Phys. 17, 141 (2024) · published 22 November 2024 | · pdf

For a significant composition range, the suppression of the spin density wave transition temperature ($T_{\text{SDW}}$) in Cr- and Mn-substituted BaFe$_{2}$As$_{2}$ (CrBFA and MnBFA, respectively) coincides as a function of Cr/Mn content, despite the distinct electronic effects of these substitutions. Additionally, for any Cr/Mn content superconductivity (SC) is absent and this topic is particularly less explored in the case of CrBFA. In this work, we employ angle-resolved photoemission spectroscopy (ARPES) and combined density functional theory plus dynamical mean field theory (DFT+DMFT) to address the evolution of the Fermi surface (FS) and electronic correlations in CrBFA. Our findings reveal that incorporating Cr leads to an effective hole doping of the states near the FS, which is well described within the virtual crystal approximation (VCA). Moreover, analysis of the ARPES spectra of the bands with main $d_{yz}$-orbital character reveals a fractional scaling of the imaginary part of self-energy as a function of the binding energy, a signature property of Hund's correlations. Our DFT+DMFT calculations support these experimental findings. We conclude that CrBFA is a correlated electron system for which the changes in the FS as a function of Cr are unrelated to the suppression of $T_{\text{SDW}}$. In addition, we suggest that the absence of SC is primarily due to the competition between Cr local moments and the Fe-derived itinerant spin fluctuations.
The superconducting clock-circuit: Improving the coherence of Josephson radiation beyond the thermodynamic uncertainty relation

David Scheer, Jonas Völler, Fabian Hassler

SciPost Phys. 17, 140 (2024) · published 21 November 2024 | · pdf

In the field of superconducting electronics, the on-chip generation of AC radiation is essential for further advancements. Although a Josephson junction can emit AC radiation from a purely DC voltage bias, the coherence of this radiation is significantly limited by Johnson-Nyquist noise. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings indicate that the thermodynamic uncertainty relation can be broken by a classical pendulum clock. We demonstrate how the violation of the TUR can be used as a design principle for radiation sources by showing that a superconducting clock circuit emits coherent AC radiation from a DC bias.
Out-of-equilibrium full counting statistics in Gaussian theories of quantum magnets

Riccardo Senese, Jacob H. Robertson, Fabian H. L. Essler

SciPost Phys. 17, 139 (2024) · published 20 November 2024 | · pdf

We consider the probability distributions of the subsystem (staggered) magnetization in ordered and disordered models of quantum magnets in D dimensions. We focus on Heisenberg antiferromagnets and long-range transverse-field Ising models as particular examples. By employing a range of self-consistent time-dependent mean-field approximations in conjunction with Holstein-Primakoff, Dyson-Maleev, Schwinger boson and modified spin-wave theory representations we obtain results in thermal equilibrium as well as during non-equilibrium evolution after quantum quenches. To extract probability distributions we derive a simple formula for the characteristic function of generic quadratic observables in any Gaussian theory of bosons.
On the Virasoro fusion and modular kernels at any irrational central charge

Julien Roussillon

SciPost Phys. 17, 138 (2024) · published 20 November 2024 | · pdf

We propose a series representation for the Virasoro fusion and modular kernels at any irrational central charge. Two distinct, yet closely related formulas are needed for the cases $c∈ \mathbb{C} \backslash (-∞,1]$ and $c <1$. Our proposal for $c <1$ agrees numerically with the fusion transformation of the four-point spherical conformal blocks, whereas our proposal for $c∈ \mathbb{C} \backslash (-∞,1]$ agrees numerically with Ponsot and Teschner's integral formula for the fusion kernel. The case of the modular kernel is studied as a special case of the fusion kernel.
Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders

Pei-Yun Yang, Yu-Chin Tzeng

SciPost Phys. Core 7, 074 (2024) · published 20 November 2024 | · pdf

Quantum entanglement plays a crucial role not only in understanding Hermitian many-body systems but also in offering valuable insights into non-Hermitian quantum systems. In this paper, we analytically investigate the entanglement Hamiltonian and entanglement energy spectrum of a non-Hermitian spin ladder using perturbation theory in the biorthogonal basis. Specifically, we examine the entanglement properties between coupled non-Hermitian quantum spin chains. In the strong coupling limit ($J_\mathrm{rung}\gg1$), first-order perturbation theory reveals that the entanglement Hamiltonian closely resembles the single-chain Hamiltonian with renormalized coupling strengths, allowing for the definition of an ad hoc temperature. Our findings provide new insights into quantum entanglement in non-Hermitian systems and offer a foundation for developing novel approaches for studying finite temperature properties in non-Hermitian quantum many-body systems.
Topological dipole insulator

Ho Tat Lam, Jung Hoon Han, Yizhi You

SciPost Phys. 17, 137 (2024) · published 18 November 2024 | · pdf

We expand the concept of two-dimensional topological insulators to encompass a novel category known as topological dipole insulators (TDIs), characterized by conserved dipole moments along the $x$-direction in addition to charge conservation. By generalizing Laughlin's flux insertion argument, we prove a no-go theorem and predict possible edge patterns and anomalies in a TDI with both charge $U^e(1)$ and dipole $U^d(1)$ symmetries. The edge of a TDI is characterized as a quadrupolar channel that displays a dipole $U^d(1)$ anomaly. A quantized amount of dipole gets transferred between the edges under the dipolar flux insertion, manifesting as 'quantized quadrupolar Hall effect' in TDIs. A microscopic coupled-wire Hamiltonian realizing the TDI is constructed by introducing a mutually commuting pair-hopping terms between wires to gap out all the bulk modes while preserving the dipole moment. The effective action at the quadrupolar edge can be derived from the wire model, with the corresponding bulk dipolar Chern-Simons response theory delineating the topological electromagnetic response in TDIs. Finally, we enrich our exploration of topological dipole insulators to the spinful case and construct a dipolar version of the quantum spin Hall effect, whose boundary evidences a mixed anomaly between spin and dipole symmetry. Effective bulk and the edge action for the dipolar quantum spin Hall insulator are constructed as well.
Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems

Da-Chuan Lu, Zhengdi Sun, Yi-Zhuang You

SciPost Phys. 17, 136 (2024) · published 15 November 2024 | · pdf

In this paper, we study the twisted gauging on the (1+1)d lattice and construct various non-local mappings on the lattice operators. To be specific, we define the twisted Gauss law operator and implement the twisted gauging of the finite group on the lattice motivated by the orbifolding procedure in the conformal field theory, which involves the data of non-trivial element in the second cohomology group of the gauge group. We show the twisted gauging is equivalent to the two-step procedure of first applying the SPT entangler and then untwisted gauging. We use the twisted gauging to construct the triality (order 3) and $p$-ality (order $p$) mapping on the $\mathbb{Z}_p× \mathbb{Z}_p$ symmetric Hamiltonians, where $p$ is a prime. Such novel non-local mappings generalize Kramers-Wannier duality and they preserve the locality of symmetric operators but map charged operators to non-local ones. We further construct quantum process to realize these non-local mappings and analyze the induced mappings on the phase diagrams. For theories that are invariant under these non-local mappings, they admit the corresponding non-invertible symmetries. The non-invertible symmetry will constrain the theory at the multicritical point between the gapped phases. We further give the condition when the non-invertible symmetry can have symmetric gapped phase with a unique ground state.
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.
3d gravity from Virasoro TQFT: Holography, wormholes and knots

Scott Collier, Lorenz Eberhardt, Mengyang Zhang

SciPost Phys. 17, 134 (2024) · published 14 November 2024 | · pdf

We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper [SciPost Phys. 15, 151 (2023)]. We compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions. This matching is highly non-trivial, but can be checked directly in some examples. We then showcase the formalism in action, by computing the gravity partition functions of many relevant topologies. For holographic applications, we focus on the partition functions of Euclidean multi-boundary wormholes with three-punctured spheres as boundaries. This precisely quantifies the higher moments of the structure constants in the proposed ensemble boundary dual and subjects the proposal to thorough checks. Finally, we investigate in detail the example of the figure eight knot complement as a hyperbolic 3-manifold. We show that the Virasoro TQFT partition function is identical to the partition function computed in Teichmüller theory, thus giving strong evidence for the equivalence of these TQFTs. We also show how to produce a large class of manifolds via Dehn surgery on the figure eight knot.

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