Adiabatic dynamics of many-body systems close to a quantum critical point

We show that a closed quantum system driven through a quantum critical point with two rates ${\ensuremath{\omega}}_{1}$ (which controls its proximity to the quantum critical point) and ${\ensuremath{\omega}}_{2}$ (which controls the dispersion of the low-energy quasiparticles at the critical point) exhibits novel scaling laws for defect density $n$ and residual energy $Q$ . We demonstrate suppression of both $n$ and $Q$ with increasing ${\ensuremath{\omega}}_{2}$ leading to an alternate route to achieving near-adiabaticity in a finite time for a quantum system during its passage through a critical point. We provide an exact solution for such dynamics with linear drive protocols applied to a class of integrable models, supplement this solution with scaling arguments applicable to generic many-body Hamiltonians, and discuss specific models and experimental systems where our theory may be tested.We show that a closed quantum system driven through a quantum critical point with two rates ${\ensuremath{\omega}}_{1}$ (which controls its proximity to the quantum critical point) and ${\ensuremath{\omega}}_{2}$ (which controls the dispersion of the low-energy quasiparticles at the critical point) exhibits novel scaling laws for defect density $n$ and residual energy $Q$. We demonstrate suppression of both $n$ and $Q$ with increasing ${\ensuremath{\omega}}_{2}$ leading to an alternate route to achieving near-adiabaticity in a finite time for a quantum system during its passage through a critical point. We provide an exact solution for such dynamics with linear drive protocols applied to a class of integrable models, supplement this solution with scaling arguments applicable to generic many-body Hamiltonians, and discuss specific models and experimental systems where our theory may be tested.

arXiv:1402.4805Physical Review BSep 22, 201425 citations

Out-of-equilibrium dynamics in many-body quantum systems

Laurent Sanchez-Palencia

Aug 1, 20140 citations

Scaling in driven dynamics starting in the vicinity of a quantum critical point

Shuai Yin, Chung-Yu Lo, Pochung Chen

Driven dynamics across a quantum critical point is usually described by the Kibble-Zurek scaling. Although the original Kibble-Zurek scaling requires an adiabatic initial state, it has been shown that scaling behaviors exist even when the driven dynamics is triggered from a thermal equilibrium state exactly at the critical point, in spite of the breakdown of the initial adiabaticity. In this paper, we show that the existence of the scaling behavior can be generalized to the case of the initial state being a thermal equilibrium state near the critical point. We propose a scaling theory in which the initial parameters are included as additional scaling variables due to the breakdown of the initial adiabaticity. In particular, we demonstrate that for the driven critical dynamics in a closed system, the nontrivial thermal effects are closely related to the initial distance to the critical point. We numerically confirm the scaling theory by simulating the real-time dynamics of the one-dimensional quantum Ising model at both zero and finite temperatures.Driven dynamics across a quantum critical point is usually described by the Kibble-Zurek scaling. Although the original Kibble-Zurek scaling requires an adiabatic initial state, it has been shown that scaling behaviors exist even when the driven dynamics is triggered from a thermal equilibrium state exactly at the critical point, in spite of the breakdown of the initial adiabaticity. In this paper, we show that the existence of the scaling behavior can be generalized to the case of the initial state being a thermal equilibrium state near the critical point. We propose a scaling theory in which the initial parameters are included as additional scaling variables due to the breakdown of the initial adiabaticity. In particular, we demonstrate that for the driven critical dynamics in a closed system, the nontrivial thermal effects are closely related to the initial distance to the critical point. We numerically confirm the scaling theory by simulating the real-time dynamics of the one-dimensional quantum Ising model at both zero and finite temperatures.

arXiv:1607.01840Physical review. B./Physical review. BAug 25, 201611 citations

Quantum dynamical phase transition in a system with many-body interactions

Ernesto P. Danieli, Gonzalo A. Álvarez, Patricia R. Levstein +1 more

arXiv:cond-mat/0511639Solid State CommunicationsNov 17, 200628 citations

Local shortcut to adiabaticity for quantum many-body systems

Victor Mukherjee, Simone Montangero, Rosario Fazio

We study the environmentally assisted local transitionless dynamics in closed spin systems driven through quantum critical points. In general the shortcut to adaiabaticity (STA) in quantum critical systems requires highly nonlocal control Hamiltonians. In this work we develop an approach to achieve local shortcuts to adiabaticity (LSTA) in spin chains, using local control fields which scale polynomially with the system size, following universal critical exponents. We relate the control fields to reduced fidelity susceptibility and use the transverse Ising model in one dimension to exemplify our generic results. We also extend our analysis to achieve LSTA in central spin models.We study the environmentally assisted local transitionless dynamics in closed spin systems driven through quantum critical points. In general the shortcut to adaiabaticity (STA) in quantum critical systems requires highly nonlocal control Hamiltonians. In this work we develop an approach to achieve local shortcuts to adiabaticity (LSTA) in spin chains, using local control fields which scale polynomially with the system size, following universal critical exponents. We relate the control fields to reduced fidelity susceptibility and use the transverse Ising model in one dimension to exemplify our generic results. We also extend our analysis to achieve LSTA in central spin models.

arXiv:1603.05057Physical Review AJun 7, 201625 citations

n

and residual energy

Q

. We demonstrate suppression of both

n

and

Q

with increasing ${\ensuremath{\omega}}_{2}$ leading to an alternate route to achieving near-adiabaticity in a finite time for a quantum system during its passage through a critical point. We provide an exact solution for such dynamics with linear drive protocols applied to a class of integrable models, supplement this solution with scaling arguments applicable to generic many-body Hamiltonians, and discuss specific models and experimental systems where our theory may be tested.