Publications

Order by: publication date number of citations

• Quantum current and holographic categorical symmetry

  Tian Lan, Jing-Ren Zhou

  SciPost Phys. 16, 053 (2024) · published 23 February 2024 | Toggle abstract · pdf

  We establish the formulation for quantum current. Given a symmetry group G, let $\mathcal{C}$:=Rep G be its representation category. Physically, symmetry charges are objects of $\mathcal{C}$ and symmetric operators are morphisms in $\mathcal{C}$. The addition of charges is given by the tensor product of representations. For any symmetric operator O crossing two subsystems, the exact symmetry charge transported by O can be extracted. The quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. A quantum current exactly corresponds to an object in the Drinfeld center $Z_1(\mathcal{C})$. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension. To express the local conservation, the internal hom must be used to compute the charge difference, and the framework of enriched category is inevitable. To illustrate these ideas, we develop a rigorous scheme of renormalization in one-dimensional lattice systems and analyse the fixed-point models. It is proved that in the fixed-point models, superconducting quantum currents form a Lagrangian algebra in $Z_1(\mathcal{C})$ and the boundary-bulk correspondence is verified in the enriched setting. Overall, the quantum current provides a natural physical interpretation to the holographic categorical symmetry.

• A solvable model for graph state decoherence dynamics

  Jérôme Houdayer, Haggai Landa, Grégoire Misguich

  SciPost Phys. Core 7, 009 (2024) · published 23 February 2024 | Toggle abstract · pdf

  We present an exactly solvable toy model for the continuous dissipative dynamics of permutation-invariant graph states of $N$ qubits. Such states are locally equivalent to an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state, a fundamental resource in many quantum information processing setups. We focus on the time evolution of the state governed by a Lindblad master equation with the three standard single-qubit jump operators, the Hamiltonian part being set to zero. Deriving analytic expressions for the expectation values of observables expanded in the Pauli basis at all times, we analyze the nontrivial intermediate-time dynamics. Using a numerical solver based on matrix product operators, we simulate the time evolution for systems with up to 64 qubits and verify a numerically exact agreement with the analytical results. We find that the evolution of the operator space entanglement entropy of a bipartition of the system manifests a plateau whose duration increases logarithmically with the number of qubits, whereas all Pauli-operator products have expectation values decaying at most in constant time.

• Entanglement Rényi entropies from ballistic fluctuation theory: The free fermionic case

  Giuseppe del Vecchio del Vecchio, Benjamin Doyon, Paola Ruggiero

  SciPost Phys. Core 7, 005 (2024) · published 14 February 2024 | Toggle abstract · pdf

  The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of branch-point twist fields, the starting point for computing Rényi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of Rényi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations.

  1 citation

• Quantifying non-stabilizerness via information scrambling

  Arash Ahmadi, Eliska Greplova

  SciPost Phys. 16, 043 (2024) · published 8 February 2024 | Toggle abstract · pdf

  The advent of quantum technologies brought forward much attention to the theoretical characterization of the computational resources they provide. A method to quantify quantum resources is to use a class of functions called magic monotones and stabilizer entropies, which are, however, notoriously hard and impractical to evaluate for large system sizes. In recent studies, a fundamental connection between information scrambling, the magic monotone mana and 2-Renyi stabilizer entropy was established. This connection simplified magic monotone calculation, but this class of methods still suffers from exponential scaling with respect to the number of qubits. In this work, we establish a way to sample an out-of-time-order correlator that approximates magic monotones and 2-Renyi stabilizer entropy. We numerically show the relation of these sampled correlators to different non-stabilizerness measures for both qubit and qutrit systems and provide an analytical relation to 2-Renyi stabilizer entropy. Furthermore, we put forward and simulate a protocol to measure the monotonic behaviour of magic for the time evolution of local Hamiltonians.

• Integrability and complexity in quantum spin chains

  Ben Craps, Marine De Clerck, Oleg Evnin, Philip Hacker

  SciPost Phys. 16, 041 (2024) · published 7 February 2024 | Toggle abstract · pdf

  There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexity in practice has remained elusive. We provide a connection of this sort by constructing a specific matrix in terms of the eigenvectors of a given quantum Hamiltonian. The null eigenvalues of this matrix are in one-to-one correspondence with conserved quantities that have simple locality properties (a hallmark of integrability). The typical magnitude of the eigenvalues, on the other hand, controls an explicit bound on Nielsen's complexity of the quantum evolution operator, defined in terms of the same locality specifications. We demonstrate how this connection works in a few concrete examples of quantum spin chains that possess diverse arrays of highly structured conservation laws mandated by integrability.

  1 citation

• The bosonic skin effect: Boundary condensation in asymmetric transport

  Louis Garbe, Yuri Minoguchi, Julian Huber, Peter Rabl

  SciPost Phys. 16, 029 (2024) · published 25 January 2024 | Toggle abstract · pdf

  We study the incoherent transport of bosonic particles through a one dimensional lattice with different left and right hopping rates, as modelled by the asymmetric simple inclusion process (ASIP). Specifically, we show that as the current passing through this system increases, a transition occurs, which is signified by the appearance of a characteristic zigzag pattern in the stationary density profile near the boundary. In this highly unusual transport phase, the local particle distribution alternates on every site between a thermal distribution and a Bose-condensed state with broken $U(1)$-symmetry. Furthermore, we show that the onset of this phase is closely related to the so-called non-Hermitian skin effect and coincides with an exceptional point in the spectrum of density fluctuations. Therefore, this effect establishes a direct connection between quantum transport, non-equilibrium condensation phenomena and non-Hermitian topology, which can be probed in cold-atom experiments or in systems with long-lived photonic, polaritonic and plasmonic excitations.

  3 citations

• Self-consistent dynamical maps for open quantum systems

  Orazio Scarlatella, Marco Schirò

  SciPost Phys. 16, 026 (2024) · published 24 January 2024 | Toggle abstract · pdf

  In several cases, open quantum systems can be successfully described using master equations relying on Born-Markov approximations, but going beyond these approaches has become often necessary. In this work, we introduce the NCA and NCA-Markov dynamical maps for open quantum systems, which go beyond these master equations replacing the Born approximation with a self-consistent approximation, known as non-crossing approximation (NCA). These maps are formally similar to master equations, but allow to capture non-perturbative effects of the environment at a moderate extra numerical cost. To demonstrate their capabilities, we apply them to the spin-boson model at zero temperature for both a Ohmic and a sub-Ohmic environment, showing that they can both qualitatively capture its strong-coupling behaviour, and be quantitatively correct beyond standard master equations.

  2 citations

• Cavity-induced bifurcation in classical rate theory

  Kalle Sulo Ukko Kansanen, Tero Tapio Heikkilä

  SciPost Phys. 16, 025 (2024) · published 23 January 2024 | Toggle abstract · pdf

  We show how coupling an ensemble of bistable systems to a common cavity field affects the collective stochastic behavior of this ensemble. In particular, the cavity provides an effective interaction between the systems, and parametrically modifies the transition rates between the metastable states. We predict that the cavity induces a phase transition at a critical temperature which depends linearly on the number of systems. It shows up as a spontaneous symmetry breaking where the stationary states of the bistable system bifurcate. We observe that the transition rates slow down independently of the phase transition, but the rate modification vanishes for alternating signs of the system-cavity couplings, corresponding to a disordered ensemble of dipoles. Our results are of particular relevance in polaritonic chemistry where the presence of a cavity has been suggested to affect chemical reactions.

• Constraints on physical computers in holographic spacetimes

  Aleksander M. Kubicki, Alex May, David Pérez-Garcia

  SciPost Phys. 16, 024 (2024) · published 23 January 2024 | Toggle abstract · pdf

  Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

  1 citation

• Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons

  Friethjof Theel, Simeon I. Mistakidis, Peter Schmelcher

  SciPost Phys. 16, 023 (2024) · published 23 January 2024 | Toggle abstract · pdf

  We study the impact of induced correlations and quasiparticle properties by immersing two distinguishable impurities in a harmonically trapped bosonic medium. It is found that when the impurities couple both either repulsively or attractively to their host, the latter mediates a two-body correlated behavior between them. In the reverse case, namely the impurities interact oppositely with the host, they feature anti-bunching. Monitoring the impurities relative distance and constructing an effective two-body model to be compared with the full many-body calculations, we are able to associate the induced (anti-) correlated behavior of the impurities with the presence of attractive (repulsive) induced interactions. Furthermore, we capture the formation of a bipolaron and a trimer state in the strongly attractive regime. The trimer refers to the correlated behavior of two impurities and a representative atom of the bosonic medium and it is characterized by an ellipsoidal shape of the three-body correlation function. Our results open the way for controlling polaron induced correlations and creating relevant bound states.

  1 citation