Publications

Order by: publication date number of citations

• Symmetry-enforced minimal entanglement and correlation in quantum spin chains

  Kangle Li, Liujun Zou

  SciPost Phys. 19, 020 (2025) · published 17 July 2025 | Toggle abstract · pdf

  The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation enforced by the $SO(3)$ spin rotation symmetry and lattice translation symmetry in a quantum spin-$J$ chain, with $J$ a positive integer. When neither symmetry is spontaneously broken, for a sufficiently long segment in a sufficiently large closed chain, we find that the minimal Rényi-$\alpha$ entropy compatible with these symmetries is $\min\{ -\frac{2}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), 2\ln(J+1) \}$, for any $\alpha∈\mathbb{R}^+$. In an infinitely long open chain with such symmetries, for any $\alpha∈\mathbb{R}^+$ the minimal Rényi-$\alpha$ entropy of half of the system is $\min\{ -\frac{1}{\alpha-1}\ln(\frac{1}{2^\alpha}({1+\frac{1}{(2J+1)^{\alpha-1}}})), \ln(J+1) \}$. When $\alpha→ 1$, these lower bounds give the symmetry-enforced minimal von Neumann entropies in these setups. Moreover, we show that no state in a quantum spin-$J$ chain with these symmetries can have a vanishing correlation length. Interestingly, the states with the minimal entanglement may not be a state with the minimal correlation length.

• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries

  Siyuan Wang, Yanyan Chen, Hongyu Wang, Yuting Hu, Yidun Wan

  SciPost Phys. 19, 018 (2025) · published 17 July 2025 | Toggle abstract · pdf

  In this paper, we apply the method of Fourier transform and basis rewriting developed in [H. Wang et al., J. High Energy Phys. 02, 030 (2020)] for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group $G$) of three-dimensional topological orders. We find that the gapped boundary condition of the gauge theory model is characterized by a Frobenius algebra in the representation category $Rep(G)$ of $G$, which also describes charge splitting and condensation on the boundary. We also show that our Fourier transform maps the three-dimensional gauge theory model with input data $G$ to the Walker-Wang model with input data $Rep(G)$ on a trivalent lattice with dangling edges, after truncating the Hilbert space by projecting all dangling edges to the trivial representation of $G$. This Fourier transform also provides a systematic construction of the gapped boundary theory of the Walker-Wang model. This establishes a correspondence between two types of topological field theories: the extended Dijkgraaf-Witten and extended Crane-Yetter theories.

• 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.

  1 citation

• Exact spin correlators of integrable quantum circuits from algebraic geometry

  Arthur Hutsalyuk, Yunfeng Jiang, Balazs Pozsgay, Hefeng Xu, Yang Zhang

  SciPost Phys. 19, 003 (2025) · published 1 July 2025 | Toggle abstract · pdf

  We calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for the calibration of quantum simulation platforms. We use the algebraic Bethe Ansatz, in combination with computational algebraic geometry, to obtain analytic results for medium-size (around 10-20 qubits) quantum circuits. The results are rational functions of the quantum circuit parameters. We obtain analytic results for such correlation functions both in the real space and Fourier space. In the real space, we analyze the short time and long time limits of the correlation functions. In Fourier space, we obtain analytic results in different parameter regimes, which exhibit qualitatively different behaviors. Using these analytic results, one can easily generate numerical data to arbitrary precision.

  2 citations

• Topological holography, quantum criticality, and boundary states

  Sheng-Jie Huang, Meng Cheng

  SciPost Phys. 18, 213 (2025) · published 30 June 2025 | Toggle abstract · pdf

  Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local dynamics of a theory and provides a unified description of the symmetry and duality in gapped and gapless phases of matter. In this work, we develop the topological holographic picture for (1+1)$d$ quantum phases, including both gapped phases as well as a wide range of quantum critical points, including phase transitions between symmetry protected topological (SPT) phases, symmetry enriched quantum critical points, deconfined quantum critical points, and intrinsically gapless SPT phases. Topological holography puts a strong constraint on the emergent symmetry and the anomaly for these critical theories. We show how the partition functions of these critical points can be obtained from dualizing (orbifolding) more familiar critical theories. The topological responses of the defect operators are also discussed in this framework. We further develop a topological holographic picture for conformal boundary states of (1+1)$d$ rational conformal field theories. This framework provides a simple physical picture to understand conformal boundary states and also uncovers the nature of the gapped phases corresponding to the boundary states.

  18 citations

• Knizhnik-Zamolodchikov equations and integrable hyperbolic Landau-Zener models

  Suvendu Barik, Lieuwe Bakker, Vladimir Gritsev, Emil A. Yuzbashyan

  SciPost Phys. 18, 212 (2025) · published 27 June 2025 | Toggle abstract · pdf

  We study the relationship between integrable Landau-Zener (LZ) models and Knizhnik-Zamolodchikov (KZ) equations. The latter are originally equations for the correlation functions of two-dimensional conformal field theories, but can also be interpreted as multi-time Schrödinger equations. The general LZ problem is to find probabilities of tunneling from eigenstates at $t=t_\text{in}$ to eigenstates at $t\to+∞$ for an $N× N$ time-dependent Hamiltonian $\hat H(t)$. A number of such problems are exactly solvable in the sense that their tunneling probabilities are elementary functions of Hamiltonian parameters. Recently, it has been proposed that exactly solvable LZ models of this type map to KZ equations. Here we use this connection to identify and solve a class of integrable LZ models with hyperbolic time dependence, $\hat H(t)=\hat A+\hat B/t$, for $N=2, 3$, and $4$, where $\hat A$ and $\hat B$ are time-independent matrices.

  1 citation

• Theorems for the lightcone bootstrap

  Balt C. van Rees

  SciPost Phys. 18, 207 (2025) · published 26 June 2025 | Toggle abstract · pdf

  Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE coefficients at large spin and fixed twist always become that of a generalized free field theory.

  3 citations

• Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons

  Eric Palmerduca, Hong Qin

  SciPost Phys. 18, 188 (2025) · published 16 June 2025 | Toggle abstract · pdf

  The past decades have seen substantial interest in the so-called orbital angular momentum (OAM) of light, driven largely by its diverse range of applications. However, there are fundamental theoretical issues with decomposing the angular momentum of massless particles, such as photons, into spin (SAM) and orbital angular momentum parts. While the angular momentum of massive particles has a natural splitting into the Wigner SAM and OAM, there are numerous proposed splittings for photons and no consensus about which is correct. Moreover, it has been shown that most of the proposed SAM and OAM operators do not satisfy the defining commutation relations of angular momentum operators and are thus not legitimate splittings. Here, we prove that it is generally impossible to split the total angular momentum operator of massless bosons, such as photons and gravitons, into spin and orbital parts. We prove two further generalizations of this result, showing that there are no SAM-OAM splittings even if (1) the SAM operator generates non-internal symmetries or (2) if one allows the SAM and OAM operators to generate non-SO(3) symmetries.

  2 citations

• Bethe Ansatz, quantum circuits, and the F-basis

  Roberto Ruiz, Alejandro Sopena, Esperanza López, Germán Sierra, Balázs Pozsgay

  SciPost Phys. 18, 187 (2025) · published 12 June 2025 | Toggle abstract · pdf

  The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the spin-$1/2$ XXZ model. These circuits represent a unitary formulation of the standard algebraic Bethe Ansatz, expressed using matrix-product states that act on both the spin chain and an auxiliary space. In this work, we systematize these previous results, and show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. The new basis, identical to the "F-basis" known from the theory of quantum-integrable models, generates the linear superposition of plane waves that is characteristic of the coordinate Bethe Ansatz. We explain this connection, highlighting that certain properties of the F-basis (namely, the exchange symmetry of the spins) are crucial for the construction of algebraic Bethe circuits. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-$1/2$ XXZ model.

  4 citations

• Classical weight-four L-value ratios as sums of Calabi-Yau invariants

  Philip Candelas, Xenia de la Ossa, Joseph McGovern

  SciPost Phys. 18, 181 (2025) · published 6 June 2025 | Toggle abstract · pdf

  We revisit the series solutions of the attractor equations of 4d $\mathcal{N}=2$ supergravities obtained by Calabi–Yau compactifications previously studied in [P. Candelas et al., J. High Energy Phys. 11, 032 (2021)]. While only convergent for a restricted set of black hole charges, we find that they are summable with Padé resummation providing a suitable method. By specialising these solutions to rank-two attractors, we obtain many conjectural identities of the type discovered in [P. Candelas et al., J. High Energy Phys. 11, 032 (2021)]. These equate ratios of weight-four special L-values with an infinite series whose summands are formed out of genus-0 Gromov–Witten invariants. We also present two new rank-two attractors which belong to moduli spaces each interesting in their own right. Each of these moduli spaces possess two points of maximal unipotent monodromy. One has already been studied by Hosono and Takagi, and we discuss issues stemming from the associated L-function having nonzero rank.