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We formulate dynamical phase transitions in subsystems embedded in larger quantum systems. Introducing the entanglement echo as an overlap of the initial and instantaneous entanglement ground states, we show its analytic structure after a quench provides natural definition of dynamical phase transitions in the subsystem. These transitions come in two varieties, the entanglement-type transitions and the bulk-type Loschmidt transitions. The entanglement-type transitions arise from periodic reorganization of quantum correlations between the subsystem and its environment, manifesting in instantaneous entanglement ground state degeneracies. Furthermore, the entanglement echo distinguishes the direction of the quench, resolves spatially distinct dynamical phase transitions for non-uniform quenches and give rise to sharply-defined transitions for mixed initial states. We propose an experimental probe to identify entanglement-type transitions through temporal changes in subsystem fluctuations.
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We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum dynamics in the enlarged Hilbert space of an embedding quantum simulator. In this manner, entanglement monotones are conveniently mapped onto physical observables, overcoming the necessity of full tomography and reducing drastically the experimental requirements. Furthermore, this method is directly applicable to pure states and, assisted by classical algorithms, to the mixed-state case. Finally, we expect that the proposed embedding framework paves the way for a general theory of enhanced one-to-one quantum simulators.
We propose a quantum algorithm in an embedding ion-trap quantum simulator for the efficient computation of N-qubit entanglement monotones without the necessity of full tomography. Moreover, we discuss possible realistic scenarios and study the associated decoherence mechanisms.
The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture that is valid for short-range interactions. Our results will allow experimental studies of a wide range of phenomena, such as quantum transport, thermalisation, localisation and entanglement growth, and represent a first step towards a new quantum-optical regime with on-demand quasiparticles with tunable non-linear interactions.
Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics. However, exact analytical results remain scarce, especially for systems out of equilibrium. In this work we examine a paradigmatic one-dimensional fermionic system that consists of a uniform tight-binding chain with an arbitrary scattering region near its center, which is subject to a DC bias voltage at zero temperature. The system is thus held in a current-carrying nonequilibrium steady state, which can nevertheless be described by a pure quantum state. Using a generalization of the Fisher-Hartwig conjecture, we present an exact calculation of the bipartite entanglement entropy of a subsystem with its complement, and show that the scaling of entanglement with the length of the subsystem is highly unusual, containing both a volume-law linear term and a logarithmic term. The linear term is related to imperfect transmission due to scattering, and provides a generalization of the Levitov-Lesovik full counting statistics formula. The logarithmic term arises from the Fermi discontinuities in the distribution function. Our analysis also produces an exact expression for the particle-number-resolved entanglement. We find that although to leading order entanglement equipartition applies, the first term breaking it grows with the size of the subsystem, a novel behavior not observed in previously studied systems. We apply our general results to a concrete model of a tight-binding chain with a single impurity site, and show that the analytical expressions are in good agreement with numerical calculations. The analytical results are further generalized to accommodate the case of multiple scattering regions.
Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. However, not all systems fall into this category, with many body localization providing a generic mechanism for thermalization to fail in strongly disordered systems. Many-body localized (MBL) systems remain perfect insulators at non-zero temperature, which do not thermalize and therefore cannot be described using statistical mechanics. In this Colloquium we review recent theoretical and experimental advances in studies of MBL systems, focusing on the new perspective provided by entanglement and non-equilibrium experimental probes such as quantum quenches. Theoretically, MBL systems exhibit a new kind of robust integrability: an extensive set of quasi-local integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization. A description based on quasi-local integrals of motion is used to predict dynamical properties of MBL systems, such as the spreading of quantum entanglement, the behavior of local observables, and the response to external dissipative processes. Furthermore, MBL systems can exhibit eigenstate transitions and quantum orders forbidden in thermodynamic equilibrium. We outline the current theoretical understanding of the quantum-to-classical transition between many-body localized and ergodic phases, and anomalous transport in the vicinity of that transition. Experimentally, synthetic quantum systems, which are well-isolated from an external thermal reservoir, provide natural platforms for realizing the MBL phase. We review recent experiments with ultracold atoms, trapped ions, superconducting qubits, and quantum materials, in which different signatures of many-body localization have been observed. We conclude by listing outstanding challenges and promising future research directions.
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