Publications

Order by: publication date number of citations

• Complexity is not enough for randomness

  Shiyong Guo, Martin Sasieta, Brian Swingle

  SciPost Phys. 17, 151 (2024) · published 4 December 2024 | Toggle abstract · pdf

  We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium thermal partition function, and provide a set of conditions that guarantee a linear time to design. We relate the trace distance to design to spectral properties of the time-evolution operator. We apply these considerations to the Brownian $p$-SYK model as a function of the degree of locality $p$. We show that the time to design is linear, with a slope proportional to $1/p$. We corroborate that when $p$ is of order the system size this reproduces the behavior of a completely non-local Brownian model of random matrices. For the random matrix model, we reinterpret these results from the point of view of classical Brownian motion in the unitary manifold. Therefore, we find that the generation of randomness typically persists for exponentially long times in the system size, even for systems governed by highly non-local time-dependent Hamiltonians. We conjecture this to be a general property: there is no efficient way to generate approximate Haar random unitaries dynamically, unless a large degree of fine-tuning is present in the ensemble of time-dependent Hamiltonians. We contrast the slow generation of randomness to the growth of quantum complexity of the time-evolution operator. Using known bounds on circuit complexity for unitary designs, we obtain a lower bound determining that complexity grows at least linearly in time for Brownian systems. We argue that these bounds on circuit complexity are far from tight and that complexity grows at a much faster rate, at least for non-local systems.

  6 citations

• Quenching the Kitaev honeycomb model

  Louk Rademaker

  SciPost Phys. 7, 071 (2019) · published 29 November 2019 | Toggle abstract · pdf

  I studied the non-equilibrium response of an initial N\'{e}el state under time evolution with the Kitaev honeycomb model. With isotropic interactions ($J_x = J_y = J_z$) the system quickly loses its antiferromagnetic order and crosses over into a steady state valence bond solid, which can be inferred from the long-range dimer correlations. There is no signature of a dynamical phase transition. Upon including anisotropy ($J_x = J_y \neq J_z$), an exponentially long prethermal regime appears with persistent magnetization oscillations whose period derives from an effective toric code.

  6 citations

• Electric conductivity in non-Hermitian holography

  Zhuo-Yu Xian, David Rodríguez Fernández, Zhaohui Chen, Yang Liu, René Meyer

  SciPost Phys. 16, 004 (2024) · published 5 January 2024 | Toggle abstract · pdf

  We study the phase structure and charge transport at finite temperature and chemical potential in the non-Hermitian $\mathcal{PT}$-symmetric holographic model of [SciPost Phys. 9, 032 (2020)]. The non-Hermitian $\mathcal{PT}$-symmetric deformation is realized by promoting the parameter of a global U(1) symmetry to a complex number. Depending on the strength of the deformation, we find three phases: stable $\mathcal{PT}$-symmetric phase, unstable $\mathcal{PT}$-symmetric phase, and an unstable $\mathcal{PT}$-symmetry broken phase. In the three phases, the square of the condensate and also the spectral weight of the AC conductivity at zero frequency are, respectively, positive, negative, and complex. We check that the Ferrell-Glover-Tinkham sum rule for the AC conductivity holds in all the three phases. We also investigate a complexified U(1) rotor model with $\mathcal{PT}$-symmetric deformation, derive its phase structure and condensation pattern, and find a zero frequency spectral weight analogous to the holographic model.

  6 citations

• Symmetries and topological operators, on average

  Andrea Antinucci, Giovanni Galati, Giovanni Rizi, Marco Serone

  SciPost Phys. 15, 125 (2023) · published 29 September 2023 | Toggle abstract · pdf

  We study Ward identities and selection rules for local correlators in disordered theories where a 0-form global symmetry of a QFT is explicitly broken by a random coupling $h$ but it re-emerges after quenched average. We consider $h$ space-dependent or constant. In both cases we construct the symmetry operator implementing the group action, topological after average. In the first case, relevant in statistical systems with random impurities, such symmetries can be coupled to external backgrounds and can be gauged, like ordinary symmetries in QFTs. We also determine exotic selection rules arising when symmetries emerge after average in the IR, explaining the origin of LogCFTs from symmetry considerations. In the second case, relevant in AdS/CFT to describe the dual boundary theory of certain bulk gravitational theories, the charge operator is not purely codimension-1, it can be defined only on homologically trivial cycles and on connected spaces. Selection rules for average correlators exist, yet such symmetries cannot be coupled to background gauge fields in ordinary ways and cannot be gauged. When the space is disconnected, in each connected component charge violation occurs, as expected from Euclidean wormholes in the bulk theory. Our findings show the obstruction to interpret symmetries emergent after average as gauged in the bulk.

  6 citations

• An index for quantum integrability

  Shota Komatsu, Raghu Mahajan, Shu-Heng Shao

  SciPost Phys. 7, 065 (2019) · published 26 November 2019 | Toggle abstract · pdf

  The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization. We define an integrability index $\mathcal{I}(J)$ for each spin $J$, with the property that $\mathcal{I}(J)$ is a lower bound on the number of quantum conserved currents of spin $J$. In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins. We apply our techniques to the $\mathbb{CP}^{N-1}$ model, the $O(N)$ model, and the flag sigma model $\frac{U(N)}{U(1)^{N}}$. For the $O(N)$ model, we establish the existence of a spin-6 quantum conserved current, in addition to the well-known spin-4 current. The indices for the $\mathbb{CP}^{N-1}$ model for $N>2$ are all non-positive, consistent with the fact that these models are not integrable. The indices for the flag sigma model $\frac{U(N)}{U(1)^{N}}$ for $N>2$ are all negative. Thus, it is unlikely that the flag sigma models are integrable.

  6 citations

• Optimal control strategies for parameter estimation of quantum systems

  Quentin Ansel, Etienne Dionis, Dominique Sugny

  SciPost Phys. 16, 013 (2024) · published 17 January 2024 | Toggle abstract · pdf

  Optimal control theory is an effective tool to improve parameter estimation of quantum systems. Different methods can be employed for the design of the control protocol. They can be based either on Quantum Fischer Information (QFI) maximization or selective control processes. We describe the similarities, differences, and advantages of these two approaches. A detailed comparative study is presented for estimating the parameters of a spin$-\tfrac{1}{2}$ system coupled to a bosonic bath. We show that the control mechanisms are generally equivalent, except when the decoherence is not negligible or when the experimental setup is not adapted to the QFI. In this latter case, the precision achieved with selective controls can be several orders of magnitude better than that given by the QFI.

  6 citations

• Hidden conformal symmetries from Killing towers with an application to large-D/CFT

  Cynthia Keeler, Victoria Martin, Alankrita Priya

  SciPost Phys. 12, 170 (2022) · published 23 May 2022 | Toggle abstract · pdf

  We generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions. We build the SL(2, R) generators directly from the Killing tower, whose Killing tensors and Killing vectors enforce the separability of the equations of motion. Our construction amounts to an explicit relationship between hidden conformal symmetries and Killing tensors: we use the Killing tower to build a novel tensor equation connecting the SL(2,R) Casimir with the radial Klein-Gordon operator. For asymptotically flat black holes in four and five dimensions we recover previously known results that were obtained using the "near-region" limit and the monodromy method. We then perform a monodromy evaluation of the Klein-Gordon scalar wave equation for all Kerr-(A)dS black holes, finding explicit forms for the zero mode symmetry generators. We also extend this analysis to the large-dimensional Schwarzschild black hole as a step towards buliding a Large-D/CFT correspondence.

  6 citations

• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries

  Benoit Estienne, Yacine Ikhlef, Andrei Rotaru

  SciPost Phys. 12, 141 (2022) · published 29 April 2022 | Toggle abstract · pdf

  We consider the entanglement entropy in critical one-dimensional quantum systems with open boundary conditions. We show that the second Rényi entropy of an interval away from the boundary can be computed exactly, provided the same conformal boundary condition is applied on both sides. The result involves the annulus partition function. We compare our exact result with numerical computations for the critical quantum Ising chain with open boundary conditions. We find excellent agreement, and we analyse in detail the finite-size corrections, which are known to be much larger than for a periodic system.

  6 citations

• Near-extremal limits of warped black holes

  Ankit Aggarwal, Alejandra Castro, Stéphane Detournay, Beatrix Mühlmann

  SciPost Phys. 15, 083 (2023) · published 7 September 2023 | Toggle abstract · pdf

  A holographic description of three-dimensional warped black holes suffers from ambiguities due to a seemingly harmless choice of coordinate system. This gives rise to the notion of ensembles in warped black holes, and we focus on two of them: the canonical and quadratic ensemble. Our aim is to quantify the imprint of these ensembles in the near-extremal limit of a warped black hole. To this end, for each ensemble, we explore the thermodynamic response and evaluate greybody factors. We also set-up a holographic dictionary in their near-AdS$_2$ region, and decode aspects of the dual near-CFT$_1$. This gives us different perspectives of the black hole that we can contrast and compare. On the one hand, we find perfect agreement between the near-extremal limit of the canonical ensemble warped black holes, their near-AdS$_2$ effective analysis, and a warped conformal field theory description. On the other, we are led to rule out the quadratic ensemble due to inconsistencies at the quantum level with the near-AdS$_2$ effective description.

  6 citations

• The giant graviton expansion in $AdS_5 \times S^5$

  Giorgos Eleftheriou, Sameer Murthy, Martí Rosselló

  SciPost Phys. 17, 098 (2024) · published 1 October 2024 | Toggle abstract · pdf

  The superconformal index of $\frac12$-BPS states of $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual AdS$_5 × S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics.

  6 citations