Publications

Order by: publication date number of citations

• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

  Xueda Wen, Yingfei Gu, Ashvin Vishwanath, Ruihua Fan

  SciPost Phys. 13, 082 (2022) · published 5 October 2022 | Toggle abstract · pdf

  In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven $(1+1)$ dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium quantum dynamics. The sequence of driving Hamiltonians is drawn from an independent and identically distributed random ensemble. At each driving step, the deformed Hamiltonian only involves the energy-momentum density spatially modulated at a single wavelength and therefore induces a M\"obius transformation on the complex coordinates. The non-equilibrium dynamics is then determined by the corresponding sequence of M\"obius transformations, from which the Lyapunov exponent $\lambda_L$ is defined. We use Furstenberg's theorem to classify the dynamical phases and show that except for a few \emph{exceptional points} that do not satisfy Furstenberg's criteria, the random drivings always lead to a heating phase with the total energy growing exponentially in the number of driving steps $n$ and the subsystem entanglement entropy growing linearly in $n$ with a slope proportional to central charge $c$ and the Lyapunov exponent $\lambda_L$. On the contrary, the subsystem entanglement entropy at an exceptional point could grow as $\sqrt{n}$ while the total energy remains to grow exponentially. In addition, we show that the distributions of the operator evolution and the energy density peaks are also useful characterizations to distinguish the heating phase from the exceptional points: the heating phase has both distributions to be continuous, while the exceptional points could support finite convex combinations of Dirac measures depending on their specific type. In the end, we compare the field theory results with the lattice model calculations for both the entanglement and energy evolution and find remarkably good agreement.

  25 citations

• The quantum entropy cone of hypergraphs

  Ning Bao, Newton Cheng, Sergio Hernández-Cuenca, Vincent P. Su

  SciPost Phys. 9, 067 (2020) · published 10 November 2020 | Toggle abstract · pdf

  In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.

  25 citations

• Bootstrapping MN and tetragonal CFTs in three dimensions

  Andreas Stergiou

  SciPost Phys. 7, 010 (2019) · published 17 July 2019 | Toggle abstract · pdf

  Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions. As a result, they have been studied in great detail with the $\varepsilon=4-d$ expansion and other field theory methods. The study of these theories with the nonperturbative numerical conformal bootstrap is initiated in this work. Bounds for operator dimensions are obtained and they are found to possess sharp kinks in the MN case, suggesting the existence of full-fledged CFTs. Based on the existence of a certain large-$N$ expansion in theories with MN symmetry, these are argued to be the CFTs predicted by the $\varepsilon$ expansion. In the tetragonal case no new kinks are found, consistently with the absence of such CFTs in the $\varepsilon$ expansion. Estimates for critical exponents are provided for a few cases describing phase transitions in actual physical systems. In two particular MN cases, corresponding to theories with global symmetry groups $O(2)^2\rtimes S_2$ and $O(2)^3\rtimes S_3$, a second kink is found. In the $O(2)^2\rtimes S_2$ case it is argued to be saturated by a CFT that belongs to a new universality class relevant for the structural phase transition of NbO$_2$ and paramagnetic-helimagnetic transitions of the rare-earth metals Ho and Dy. In the $O(2)^3\rtimes S_3$ case it is suggested that the CFT that saturates the second kink belongs to a new universality class relevant for the paramagnetic-antiferromagnetic phase transition of the rare-earth metal Nd.

  25 citations

• $q$th-root non-Hermitian Floquet topological insulators

  Longwen Zhou, Raditya Weda Bomantara, Shenlin Wu

  SciPost Phys. 13, 015 (2022) · published 8 August 2022 | Toggle abstract · pdf

  Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer $q$th-root of the evolution operator $U$ that describes Floquet topological matter. We further apply our $q$th-rooting procedure to obtain $2^n$th- and $3^n$th-root first- and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies $±(0, 1,...2^n)π/2^n$ and $±(0, 1,..., 3^n)π/3^n$, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.

  25 citations

• Isospin asymmetry in holographic baryonic matter

  Nicolas Kovensky, Andreas Schmitt

  SciPost Phys. 11, 029 (2021) · published 12 August 2021 | Toggle abstract · pdf

  We study baryonic matter with isospin asymmetry, including fully dynamically its interplay with pion condensation. To this end, we employ the holographic Witten-Sakai-Sugimoto model and the so-called homogeneous ansatz for the gauge fields in the bulk to describe baryonic matter. Within the confined geometry and restricting ourselves to the chiral limit, we map out the phase structure in the presence of baryon and isospin chemical potentials, showing that for sufficiently large chemical potentials condensed pions and isospin-asymmetric baryonic matter coexist. We also present first results of the same approach in the deconfined geometry and demonstrate that this case, albeit technically more involved, is better suited for comparisons with and predictions for real-world QCD. Our study lays the ground for future improved holographic studies aiming towards a realistic description of charge neutral, beta-equilibrated matter in compact stars, and also for more refined comparisons with lattice studies at nonzero isospin chemical potential.

  25 citations

• On the separation of Hall and Ohmic nonlinear responses

  Stepan S. Tsirkin, Ivo Souza

  SciPost Phys. Core 5, 039 (2022) · published 8 August 2022 | Toggle abstract · pdf

  The symmetric and antisymmetric parts of the linear conductivity describe the dissipative (Ohmic) and nondissipative (Hall) parts of the current. The Hall current is always transverse to the applied electric field regardless of its orientation; the Ohmic current is purely longitudinal in cubic crystals, but in lower-symmetry crystals it has a transverse component whenever the field is not aligned with a principal axis. In this work, we extend that analysis beyond the linear regime. We consider all possible ways of partitioning the current at any order in the electric field without taking symmetry into account, and find that the Hall vs Ohmic decomposition is the only one that satisfies certain basic requirements. A general prescription is given for achieving that decomposition, and the case of the quadratic conductivity is analyzed in detail. By performing a symmetry analysis we find that in five of the 122 magnetic point groups the quadratic dc conductivity is purely Ohmic and even under time reversal, a type of response that is entirely disorder mediated.

  25 citations

• Higher-group symmetry in finite gauge theory and stabilizer codes

  Maissam Barkeshli, Yu-An Chen, Po-Shen Hsin, Ryohei Kobayashi

  SciPost Phys. 16, 089 (2024) · published 3 April 2024 | Toggle abstract · pdf

  A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group global symmetry and its 't Hooft anomaly for topological finite group gauge theories in $(d+1)$ space-time dimensions, including non-Abelian gauge groups and Dijkgraaf-Witten twists. We focus on the 1-form symmetry generated by invertible (Abelian) magnetic defects and the higher-form symmetries generated by invertible topological defects decorated with lower dimensional gauged symmetry-protected topological (SPT) phases. We show that due to a generalization of the Witten effect and charge-flux attachment, the 1-form symmetry generated by the magnetic defects mixes with other symmetries into a higher group. We describe such higher-group symmetry in various lattice model examples. We discuss several applications, including the classification of fermionic SPT phases in (3+1)D for general fermionic symmetry groups, where we also derive a simpler formula for the $[O_5] ∈ H^5(BG, U(1))$ obstruction that has appeared in prior work. We also show how the $d$-group symmetry is related to fault-tolerant non-Pauli logical gates and a refined Clifford hierarchy in stabilizer codes. We discover new logical gates in stabilizer codes using the $d$-group symmetry, such as a controlled Z gate in the (3+1) D $\mathbb{Z}_2$ toric code.

  25 citations

• Topological holography: The example of the D2-D4 brane system

  Nafiz Ishtiaque, Seyed Faroogh Moosavian, Yehao Zhou

  SciPost Phys. 9, 017 (2020) · published 5 August 2020 | Toggle abstract · pdf

  We propose a toy model for holographic duality. The model is constructed by embedding a stack of $N$ D2-branes and $K$ D4-branes (with one dimensional intersection) in a 6D topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2D BF theory (resp. 4D Chern-Simons theory) with $\mathrm{GL}_N$ (resp. $\mathrm{GL}_K$) gauge group. We propose that in the large $N$ limit the BF theory on $\mathbb{R}^2$ is dual to the closed string theory on $\mathbb R^2 \times \mathbb R_+ \times S^3$ with the Chern-Simons defect on $\mathbb R \times \mathbb R_+ \times S^2$. As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection -- the algebra is the Yangian of $\mathfrak{gl}_K$. We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using a D3-D5 brane configuration in type IIB -- using supersymmetric twist and $\Omega$-deformation.

  25 citations

• Snowmass2021 cosmic frontier white paper: Ultraheavy particle dark matter

  Daniel Carney, Nirmal Raj, Yang Bai, Joshua Berger, Carlos Blanco, Joseph Bramante, Christopher Cappiello, Maíra Dutra, Reza Ebadi, Kristi Engel, Edward Kolb, J. Patrick Harding, Jason Kumar, Gordan Krnjaic, Rafael F. Lang, Rebecca K. Leane, Benjamin V. Lehmann, Shengchao Li, Andrew J. Long, Gopolang Mohlabeng, Ibles Olcina, Elisa Pueschel, Nicholas L. Rodd, Carsten Rott, Dipan Sengupta, Bibhushan Shakya, Ronald L. Walsworth, Shawn Westerdale

  SciPost Phys. Core 6, 075 (2023) · published 6 November 2023 | Toggle abstract · pdf

  We outline the unique opportunities and challenges in the search for "ultraheavy" dark matter candidates with masses between roughly 10 TeV and the Planck scale $m_{\rm pl} ≈ 10^{16}$ TeV. This mass range presents a wide and relatively unexplored dark matter parameter space, with a rich space of possible models and cosmic histories. We emphasize that both current detectors and new, targeted search techniques, via both direct and indirect detection, are poised to contribute to searches for ultraheavy particle dark matter in the coming decade. We highlight the need for new developments in this space, including new analyses of current and imminent direct and indirect experiments targeting ultraheavy dark matter and development of new, ultra-sensitive detector technologies like next-generation liquid noble detectors, neutrino experiments, and specialized quantum sensing techniques.

  25 citations

• Liberating confinement from Lagrangians: 1-form symmetries and lines in 4d N=1 from 6d N=(2,0)

  Lakshya Bhardwaj, Max Hübner, Sakura Schäfer-Nameki

  SciPost Phys. 12, 040 (2022) · published 26 January 2022 | Toggle abstract · pdf

  We study confinement in 4d N=1 theories obtained by deforming 4d N=2 theories of Class S. We argue that confinement in a vacuum of the N=1 theory is encoded in the 1-cycles of the associated N=1 curve. This curve is the spectral cover associated to a generalized Hitchin system describing the profiles of two Higgs fields over the Riemann surface upon which the 6d (2,0) theory is compactified. Using our method, we reproduce the expected properties of confinement in various classic examples, such as 4d N=1 pure Super-Yang-Mills theory and the Cachazo-Seiberg-Witten setup. More generally, this work can be viewed as providing tools for probing confinement in non-Lagrangian N=1 theories, which we illustrate by constructing an infinite class of non-Lagrangian N=1 theories that contain confining vacua. The simplest model in this class is an N=1 deformation of the N=2 theory obtained by gauging $SU(3)^3$ flavor symmetry of the $E_6$ Minahan-Nemeschansky theory.

  25 citations