Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnomalies and entanglement renormalization
187
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study t Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.
rate research
Read More
Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In this work we show how to construct Gaussian bosonic quantum circuits that implement entanglement renormalization for ground states of arbitrary free bosonic chains. The construction is based on wavelet theory, and the dispersion relation of the Hamiltonian is translated into a filter design problem. We give a general algorithm that approximately solves this design problem and provide an approximation theory that relates the properties of the filters to the accuracy of the corresponding quantum circuits. Finally, we explain how the continuum limit (a free bosonic quantum field) emerges naturally from the wavelet construction.
A shallow potential well in a near-perfect quantum wire will bind a single-electron and behave like a quantum dot, giving rise to spin-dependent resonances of propagating electrons due to Coulomb repulsion and Pauli blocking. It is shown how this may be used to generate full entanglement between static and flying spin-qubits near resonance in a two-electron system via singlet or triplet spin-filtering. In a quantum wire with many electrons, the same pairwise scattering may be used to explain conductance, thermopower and shot-noise anomalies, provided the temperature/energy scale is sufficiently high for Kondo-like many-body effects to be negligible.
The folding algorithmcite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the temporal entanglement. We show that this temporal entanglement is, in many cases, equal to the spatial entanglement of a modified Hamiltonian. This inspires a modification to the folding algorithm, that we call the hybrid algorithm. We find that this leads to improved accuracy for the same numerical effort. We then use these algorithms to study relaxation in a transverse plus parallel field Ising model, finding persistent quasi-periodic oscillations for certain choices of initial conditions.
Local constraints play an important role in the effective description of many quantum systems. Their impact on dynamics and entanglement thermalization are just beginning to be unravelled. We develop a large $N$ diagrammatic formalism to exactly evaluate the bipartite entanglement of random pure states in large constrained Hilbert spaces. The resulting entanglement spectra may be classified into `phases depending on their singularities. Our closed solution for the spectra in the simplest class of constraints reveals a non-trivial phase diagram with a Marchenko-Pastur (MP) phase which terminates in a critical point with new singularities. The much studied Rydberg-blockaded/Fibonacci chain lies in the MP phase with a modified Page correction to the entanglement entropy, $Delta S_1 = 0.513595cdots$. Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained systems and provide a baseline for numerical studies.
A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through a class of variational non-Gaussian wavefunctionals for which expectation values of local operators can be efficiently calculated analytically and in a closed form. The method consists of a series of scale-dependent nonlinear canonical transformations on the fields of the theory under consideration. Here, the $lambda, phi^4$ and the sine-Gordon scalar theories are used to illustrate how non-perturbative effects far beyond the Gaussian approximation are obtained by considering the energy functional and the correlation functions of the theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
