Abstract
Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.
Highlights
Having developed the high overlap states truncation scheme, we have so far used it to construct an initial state and we have studied the properties of this approximate state
To deal with the problem for strongly non-perturbative quenches discussed in the previous section, we develop a reworking of the numerical renormalization group procedure that we refer to as the matrix element renormalization group
Even in the presence of integrability, the computation of non-equilibrium dynamics following a quantum quench remains a great challenge for theory
Summary
Non-equilibrium strongly correlated systems have been the subject of intense study over the last decade [1,2,3,4,5,6,7,8,9,10]. Analytical studies have focused on cases where the initial states are eigenstates of the Lieb-Liniger model with either c = 0 or c = ∞, due to simplifications (both cases being ‘non-interacting’ in nature) that allow one to explicitly compute overlaps between the initial state and eigenstates of the Hamiltonian governing time evolution. With these overlaps at hand, expectation values of local operators in the long-time limit can be computed via, for example, the quench action method [5, 19]. Our approach reduces the computational cost of calculations by orders of magnitude, as we will see below
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
