Publications

Order by: publication date number of citations

• Escaping fronts in local quenches of a confining spin chain

  Anna Krasznai, Gábor Takács

  SciPost Phys. 16, 138 (2024) · published 29 May 2024 | Toggle abstract · pdf

  We consider local quenches from initial states generated by a single spin-flip in either the true or the false vacuum state of the confining quantum Ising spin chain in the ferromagnetic regime. Contrary to global quenches, where the light-cone behaviour is strongly suppressed, we find a significant light-cone signal propagating with a nonzero velocity besides the expected localised oscillating component. Combining an analytic representation of the initial state with a numerical description of the relevant excitations using the two-fermion approximation, we can construct the spectrum of post-quench excitations and their overlaps with the initial state, identifying the underlying mechanism. For confining quenches built upon the true vacuum, the propagating signal consists of superpositions of left and right-moving mesons escaping confinement. In contrast, for anti-confining quenches built upon the false vacuum it is composed of superpositions of left and right-moving bubbles which escape Wannier-Stark localisation.

  3 citations

• Fermionic quantum computation with Cooper pair splitters

  Kostas Vilkelis, Antonio Manesco, Juan Daniel Torres Luna, Sebastian Miles, Michael Wimmer, Anton Akhmerov

  SciPost Phys. 16, 135 (2024) · published 27 May 2024 | Toggle abstract · pdf

  We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device consists of quantum dots tunnel-coupled by a hybrid superconducting island and a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions implements the universal set of quantum gates defined by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002)]. Due to the similarity with charge qubits, we expect charge noise to be the main source of decoherence. For this reason, we also consider an alternative design where the quantum dots have tunable coupling to the superconductor. In this second device design, we show that there is a sweet spot for which the local fermionic modes are charge neutral, making the device insensitive to charge noise effects. Finally, we compare both designs and their experimental limitations and suggest future efforts to overcome them.

  4 citations

• Physical and unphysical regimes of self-consistent many-body perturbation theory

  Kris Van Houcke, Evgeny Kozik, Riccardo Rossi, Youjin Deng, Félix Werner

  SciPost Phys. 16, 133 (2024) · published 27 May 2024 | Toggle abstract · pdf

  In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order N and plugged into the Dyson equation, which is then solved for the propagator $G_N$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_N$ converges when $N\to∞$ to a limit $G_∞\,$, which coincides with the exact physical propagator $G_{exact}$ at small enough coupling, while $G_∞ ≠ G_{exact}$ at strong coupling. This follows from the findings of [Phys. Rev. Lett. 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_∞=G_{exact}$ and $G_∞≠G_{exact}$ regimes thanks to a criterion which does not require the knowledge of $G_{exact}$, as proposed in [Phys. Rev. B 93, 161102 (2016)].

  2 citations

• Topological aspects of brane fields: Solitons and higher-form symmetries

  Salvatore D. Pace, Yu Leon Liu

  SciPost Phys. 16, 128 (2024) · published 21 May 2024 | Toggle abstract · pdf

  In this note, we classify topological solitons of $n$-brane fields, which are nonlocal fields that describe $n$-dimensional extended objects. We consider a class of $n$-brane fields that formally define a homomorphism from the $n$-fold loop space $\Omega^n X_D$ of spacetime $X_D$ to a space $\mathcal{E}_n$. Examples of such $n$-brane fields are Wilson operators in $n$-form gauge theories. The solitons are singularities of the $n$-brane field, and we classify them using the homotopy theory of ${\mathbb{E}_n}$-algebras. We find that the classification of codimension ${k+1}$ topological solitons with ${k≥ n}$ can be understood using homotopy groups of $\mathcal{E}_n$. In particular, they are classified by ${\pi_{k-n}(\mathcal{E}_n)}$ when ${n>1}$ and by ${\pi_{k-n}(\mathcal{E}_n)}$ modulo a ${\pi_{1-n}(\mathcal{E}_n)}$ action when ${n=0}$ or ${1}$. However, for ${n>2}$, their classification goes beyond the homotopy groups of $\mathcal{E}_n$ when ${k< n}$, which we explore through examples. We compare this classification to $n$-form $\mathcal{E}_n$ gauge theory. We then apply this classification and consider an ${n}$-form symmetry described by the abelian group ${G^{(n)}}$ that is spontaneously broken to ${H^{(n)}\subset G^{(n)}}$, for which the order parameter characterizing this symmetry breaking pattern is an ${n}$-brane field with target space ${\mathcal{E}_n = G^{(n)}/H^{(n)}}$. We discuss this classification in the context of many examples, both with and without 't Hooft anomalies.

  5 citations

• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects

  Luisa Eck, Paul Fendley

  SciPost Phys. 16, 127 (2024) · published 21 May 2024 | Toggle abstract · pdf

  Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. The structure yields non-invertible maps between the four models while also guaranteeing all are integrable. We construct these maps explicitly utilising topological defects coming from fusion categories and the lattice version of the orbifold construction, and use them to give explicit conformal-field-theory partition functions describing their critical regions. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy.

  17 citations

• Ground state of the staggered Heisenberg-Γ honeycomb model in a magnetic field

  Mojtaba Ahmadi-Yazdi, Mohammad-Hossein Zare, Hamid Mosadeq, Farhad Fazileh

  SciPost Phys. Core 7, 030 (2024) · published 15 May 2024 | Toggle abstract · pdf

  We study the ground state properties of the S=1/2 staggered Heisenberg-$\Gamma$ honeycomb model under a magnetic field based on analytical and numerical methods. Our calculations show that the conventional zigzag and stripy phases are favored because of the staggered Heisenberg interaction away from the pure $\Gamma$ limit. In our classical analysis, we find that the field induces a series of competing magnetic phases with relatively large unit cells in the region sandwiched between the two magnetic phases with long-range ordering. In the quantum treatment, these large magnetic unit cells are destabilized by strong quantum fluctuations that result in the stabilization of a gapless quantum spin liquid behavior. In a honeycomb $\Gamma$ magnet, we disclose an intermediate-field gapless quantum spin liquid phase driven by a tilted field away from the out-of-plane direction only for a narrow region between the low-field zigzag and high-field fully polarized phases.

• Quantum revivals in HgTe/CdTe quantum wells and topological phase transitions

  Alberto Mayorgas, Manuel Calixto, Nicolás A. Cordero, Elvira Romera, Octavio Héctor Castaños Garza

  SciPost Phys. Core 7, 029 (2024) · published 13 May 2024 | Toggle abstract · pdf

  The time evolution of a wave packet is a tool to detect topological phase transitions in two-dimensional Dirac materials, such as graphene and silicene. Here we extend the analysis to HgTe/CdTe quantum wells and study the evolution of their electron current wave packet, using 2D effective Dirac Hamiltonians and different layer thicknesses. We show that the two different periodicities that appear in this temporal evolution reach a minimum near the critical thickness, where the system goes from normal to inverted regime. Moreover, the maximum of the electron current amplitude changes with the layer thickness, identifying that current maxima reach their higher value at the critical thickness. Thus, we can characterize the topological phase transitions in terms of the periodicity and amplitude of the electron currents.

  1 citation

• Higher-group symmetry of (3+1)D fermionic $\mathbb{Z}_2$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

  Maissam Barkeshli, Po-Shen Hsin, Ryohei Kobayashi

  SciPost Phys. 16, 122 (2024) · published 7 May 2024 | Toggle abstract · pdf

  It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D $\mathbb{Z}_2$ gauge theory with an emergent fermion, and point out that pumping chiral $p+ip$ topological states gives rise to a $\mathbb{Z}_{8}$ 0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization of $T^3$ (3-torus) and $T^2 \rtimes_{C_2} S^1$ (2-torus bundle over the circle) respectively, and pumping $p+ip$ states. Our considerations also imply the possibility of a logical $T$ gate by placing the code on $\mathbb{RP}^3$ and pumping a $p+ip$ topological state.

  14 citations

• Phase transitions of wave packet dynamics in disordered non-Hermitian systems

  Helene Spring, Viktor Könye, Fabian A. Gerritsma, Ion Cosma Fulga, Anton R. Akhmerov

  SciPost Phys. 16, 120 (2024) · published 3 May 2024 | Toggle abstract · pdf

  Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition is close to 1/2 in propagating-propagating and (de)localization transitions.

  4 citations

• Monopoles in Dirac spin liquids and their symmetries from instanton calculus

  Shankar Ganesh, Joseph Maciejko

  SciPost Phys. 16, 118 (2024) · published 2 May 2024 | Toggle abstract · pdf

  The Dirac spin liquid (DSL) is a two-dimensional (2D) fractionalized Mott insulator featuring massless Dirac spinon excitations coupled to a compact U(1) gauge field, which allows for flux-tunneling instanton events described by magnetic monopoles in (2+1)D Euclidean spacetime. The state-operator correspondence of conformal field theory has been used recently to define associated monopole operators and determine their quantum numbers, which encode the microscopic symmetries of conventional ordered phases proximate to the DSL. In this work, we utilize semiclassical instanton methods not relying on conformal invariance to construct monopole operators directly in (2+1)D spacetime as instanton-induced 't Hooft vertices, i.e., fermion-number-violating effective interactions originating from zero modes of the Euclidean Dirac operator in an instanton background. In the presence of a flavor-adjoint fermion mass, resummation of the instanton gas is shown to select the correct monopole to be proliferated, in accordance with predictions of the state-operator correspondence. We also show that our instanton-based approach is able to determine monopole quantum numbers on bipartite lattices.

  1 citation