We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our is complementary to, e.g., existing methods using replica trick Witten's method of surgery, applies a generic spatial manifold genus $g$, which can be bipartitioned arbitrary way. The effects fusion braiding Wilson lines also straightforwardly studied within our framework. By considering superposition states with different line...

We study the time evolution of entanglement negativity after a local quantum quench in (1+1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their endpoints. calculate for both adjacent intervals and disjoint explicitly. For intervals, grows logarithmically right quench. After developing plateau-like feature, drops to ground-state value. case spatially separated light-cone behavior is observed evolution; addition, long-range...

Coherent control of quantum states is at the heart implementing solid-state processors and testing mechanics macroscopic level. Despite significant progress made in recent years controlling single- bi-partite systems, coherent wave function multipartite systems involving artificial qubits has been hampered due to relatively short decoherence time lacking precise methods. Here we report creation manipulation a tripartite system, which formed by superconducting qubit coupled two microscopic...

We study real-space quantum entanglement included in conformally invariant boundary states conformal field theories (CFTs). argue that essentially have no entanglement, except for constant contributions from long range topological by computing the entropy when system is bipartition into two spatial regions. From viewpoint of classical gravity duals holography, this shows are dual to trivial spacetimes zero space-time volume. also point out a continuous multiscale renormalization ansatz...

By making use of conformal mapping, we construct various time-evolution operators in (1+1)-dimensional field theories (CFTs), which take the form $\ensuremath{\int}dx\phantom{\rule{0.16em}{0ex}}f(x)\mathcal{H}(x)$, where $\mathcal{H}(x)$ is Hamiltonian density CFT and $f(x)$ an envelope function. Examples such deformed evolution include entanglement so-called sine-square deformation CFT. Within our construction, spectrum (finite-size) scaling level spacing operator are known exactly. Based...

This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization conventional topological phases matter. In such rather than considering single Hamiltonian, one considers family Hamiltonians that depend continuously on some parameters. After discussing notion we formulate bulk-boundary correspondence for an important bulk quantity, Kapustin-Spodyneiko higher Berry curvature, first in spatial dimension and then arbitrary...

An interface connecting two distinct conformal field theories hosts rich critical behaviors. In this paper, we investigate the entanglement properties of such for probing underlying universality. As inspired by holographic perspectives, demonstrate vital features various measures regarding interfaces based on several paradigmatic lattice models. Crucially, subsystems adjacent at interface, mutual information and reflected entropy exhibit identical leading logarithmic scaling, giving an...

In this work, motivated by the sine-square deformation (SSD) for (1+1)-dimensional quantum critical systems, we study non-equilibrium dynamics of a conformal field theory (CFT) with SSD, which was recently proposed to have continuous energy spectrum and Virasoro algebra. particular, time evolution entanglement entropy after quench from uniform CFT, is defined on finite space length $L$, deformed CFT. We find there crossover $t^{\ast}$ that divides into two interesting regions. For $t\ll...

Given a $generic$ two-dimensional conformal field theory (CFT), we propose an analytically solvable setup to study the Floquet dynamics of CFT, i.e., CFT subject periodic driving. A complete phase diagram in parameter space can be obtained within our setup. We find two phases: heating and non-heating phase. In phase, entanglement entropy keeps growing linearly time, indicating that system absorbing energy; oscillates periodically is not heated. At transition, grows logarithmically time...

Abstract The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in dynamical processes phase transitions systems ranging from cosmology to condensed matter and quantum materials. similarity between KZM Landau-Zener transition (LZT), which is a standard tool describe dynamics some non-equilibrium physics contemporary physics, being extensively exploited. Here we demonstrate equivalence Ising model LZT superconducting qubit system. We develop time-resolved...

In this work, we study analytically the phase transitions in quasi-periodically driven one dimensional quantum critical systems that are described by conformal field theories (CFTs). The diagrams and can be obtained using Avila's global theory one-frequency quasiperiodic cocycles. Compared to previous works where quasiperiodicity was introduced driving time no were observed [1], here propose a setup is Hamiltonians. our setup, observe heating phases, non-heating transitions. diagram as well...

Quantum impurities give rise to rich physical phenomena, with some exhibiting critical behavior described by conformal field theories (CFTs) in the low-energy limit. In parallel, party-time ($\mathcal{PT}$) symmetric non-Hermitian systems host exceptional points (EPs) at criticality, leading exotic features governed non-unitary CFTs. Here, we establish a connection between and CFTs demonstrating that properties of (1+1)-dimensional free-fermion chain central charge $c=1$ can be drastically...

In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e., band insulators with quantized conductance, using exact holographic mapping. Exact mapping is an approach to duality which maps the state a different living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and entanglement spectrum, demonstrate that dual theory of insulator. The description enables characterization system by between degrees freedom at length scales.

We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use biorthogonal basis. find that the spectrum characterizes topological properties terms existence mid-gap states Su-Schrieffer-Heeger (SSH) model with parity time-reversal symmetry (PT symmetry) Chern insulators. In addition, we at critical point PT symmetric SSH model, entropy has logarithmic scaling corresponding central charge $c=-2$. This then is free-fermion lattice realization...

In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven (1+1) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo form="postfix">)</mml:mo></mml:mrow></mml:math> dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble non-equilibrium dynamics. The sequence driving...

Microwave resonances between discrete macroscopically distinct quantum states with single photon and multiphoton absorption are observed in a strongly driven radio frequency superconducting interference device flux qubit. The amplitude of the resonant peaks dips modulated by power applied microwave irradiation population inversion is generated at low bias. These results, which can be addressed Landau–Zener transition, useful to develop an alternative means initialize manipulate qubit, as...

We study the entanglement entropy between (possibly distinct) topological phases across an interface using Abelian Chern-Simons description with boundary conditions (TBCs) at interface. From a microscopic point of view, these TBCs correspond to turning on particular gapping interactions edge modes However, in studying continuum description, we must confront problem non-factorization Hilbert space, which is standard property gauge theories. carefully define by extended space construction...

Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological support both pointlike and stringlike excitations, particular the loop (closed string) excitations may admit knotted linked In this work, we ask following question: How do different types of contribute to entanglement entropy or, alternatively, can use detect structure further obtain information underlying order? We are mainly interested order that be realized Dijkgraaf-Witten...

We report the observation of quantum jumps between macroscopic states in a superconducting phase qubit coupled to two-level systems Josephson tunnel junction, and all key features are confirmed experiments. Moreover, can be used calibrate such systems, which believed one main decoherence sources devices.

We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using continuum multi-scale ansatz (cMERA). Given ground state a Chern insulator, we construct and its cMERA paying attention, particular, to how bulk holographic geometry Berry curvature depend on properties state. It is found that each defined at different energy scale carries nonzero flux, which emanated from UV layer cMERA, towards IR. Hence, topologically nontrivial...