scholarly journals Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Etienne Granet ◽  
Maurizio Fagotti ◽  
Fabian Essler
Keyword(s):  
Form Factor ◽  
Form Factors ◽  
Transverse Field ◽  
Natural Generalization ◽  
Point Function ◽  
Quench Dynamics ◽  
Density Expansions ◽  
The One ◽  
Transverse Field Ising Model ◽  
Partial Fractions

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

Quantum quench dynamics of the one-dimensional Ising model in transverse field

Pramana ◽  
2019 ◽  
Vol 92 (4) ◽  
Author(s):  
Wei-Ke Zou ◽  
Nuo-Wei Li ◽  
Chong Han ◽  
Dong-dong Liu
Keyword(s):  
Ising Model ◽  
Transverse Field ◽  
One Dimensional ◽  
Quantum Quench ◽  
Quench Dynamics ◽  
The One

scholarly journals Efficient variational simulation of non-trivial quantum states

2019 ◽  
Vol 6 (3) ◽  
Author(s):  
Wen Wei Ho ◽  
Timothy H. Hsieh
Keyword(s):  
Transverse Field ◽  
System Size ◽  
Quantum States ◽  
Quantum Simulator ◽  
Near Term ◽  
The One ◽  
Transverse Field Ising Model ◽  
Classical Computer ◽  
Model Phase ◽  
Ordered State

We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with \bm{L}𝐋 variational parameters and physical runtimes \bm{T}𝐓 that scale linearly with the system size \bm{L}𝐋. We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational Ansätze as good descriptions of non-trivial states of matter.

scholarly journals A scattering amplitude in Conformal Field Theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marc Gillioz ◽  
Marco Meineri ◽  
João Penedones
Keyword(s):  
Field Theory ◽  
Fourier Transform ◽  
Form Factor ◽  
Conformal Field Theory ◽  
Scattering Amplitude ◽  
Form Factors ◽  
Point Function ◽  
Partial Wave Expansion ◽  
Conformal Field ◽  
The Fourier Transform

Abstract We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as p2 → 0. In particular, we study a form factor F(s, t, u) obtained from a four-point function of identical scalar primary operators. We show that F is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the 3d Ising model, perturbative fixed points and holographic CFTs.

scholarly journals Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Jonas Richter ◽  
Tjark Heitmann ◽  
Robin Steinigeweg
Keyword(s):  
Ising Model ◽  
Real Time ◽  
Transverse Field ◽  
Two Dimensional ◽  
Longitudinal Magnetization ◽  
Time Dynamics ◽  
Quantum Quenches ◽  
Many Body Systems ◽  
Quench Dynamics ◽  
Transverse Field Ising Model

We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

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