# Complexity and scaling in quantum quench in 1 + 1 dimensional fermionic field theories

@article{Liu2019ComplexityAS, title={Complexity and scaling in quantum quench in 1 + 1 dimensional fermionic field theories}, author={Sinong Liu}, journal={Journal of High Energy Physics}, year={2019}, volume={2019} }

We consider the scaling behavior of circuit complexity under quantum quench in an a relativistic fermion field theory on a one dimensional spatial lattice. This is done by finding an exactly solvable quench protocol which asymptotes to massive phases at early and late times and crosses a critical point in between. We find a variety of scaling behavior as a function of the quench rate, starting with a saturation for quenches at the lattice scale, a “fast quench scaling” at intermediate rate and…

## 7 Citations

### Quantum quench in non-relativistic fermionic field theory: harmonic traps and 2d string theory

- PhysicsJournal of High Energy Physics
- 2019

We investigate a class of exactly solvable quantum quench protocols with a finite quench rate in systems of one dimensional non-relativistic fermions in external harmonic oscillator or inverted…

### Circuit complexity near critical points

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2022

We consider the Bose–Hubbard model in two and three spatial dimensions and numerically compute the quantum circuit complexity of the ground state in the Mott insulator and superfluid phases using a…

### Quantum complexity and topological phases of matter

- PhysicsPhysical Review B
- 2022

We ﬁnd that the complexity of quantum many body states, deﬁned as a spread in the Krylov basis, may serve as a probe that distinguishes topological phases of matter. We illustrate this analytically…

### Chaos and complexity in quantum mechanics

- PhysicsPhysical Review D
- 2020

We propose a new diagnostic for quantum chaos. We show that the time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov…

### Complexity and Floquet dynamics: Nonequilibrium Ising phase transitions

- PhysicsPhysical Review B
- 2020

We study the time-dependent circuit complexity of the periodically driven transverse field Ising model using Nielsen's geometric approach. In the high-frequency driving limit the system is known to…

### Geometry and complexity of path integrals in inhomogeneous CFTs

- PhysicsJournal of High Energy Physics
- 2021

In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and…

### Circuit complexity of knot states in Chern-Simons theory

- MathematicsJournal of High Energy Physics
- 2019

We compute an upper bound on the circuit complexity of quantum states in 3d Chern-Simons theory corresponding to certain classes of knots. Specifically, we deal with states in the torus Hilbert space…

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