scholarly journals Polynomial filter diagonalization of large Floquet unitary operators

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
David J. Luitz
Keyword(s):  
Quantum Chaos ◽  
System Size ◽  
Complex Polynomial ◽  
Many Body ◽  
Unitary Evolution ◽  
Filter Diagonalization ◽  
Periodically Driven ◽  
Nonequilibrium Phenomena ◽  
Many Body Systems ◽  
Static Systems

Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies of quantum chaos, thermalization, many-body localization and time crystals, the properties of eigenvectors and eigenvalues of the unitary evolution operator, and their scaling with physical system size LL are of interest. While for static systems, powerful methods for the partial diagonalization of the Hamiltonian were developed, the unitary eigenproblem remains daunting. % In this paper, we introduce a Krylov space diagonalization method to obtain exact eigenpairs of the unitary Floquet operator with eigenvalue closest to a target on the unit circle. Our method is based on a complex polynomial spectral transformation given by the geometric sum, leading to rapid convergence of the Arnoldi algorithm. We demonstrate that our method is much more efficient than the shift invert method in terms of both runtime and memory requirements, pushing the accessible system sizes to the realm of 20 qubits, with Hilbert space dimensions \geq 10^6≥106.

scholarly journals Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

2019 ◽  
Vol 10 (1) ◽  
pp. 337-356 ◽  
Author(s):  
Zi-Xiang Li ◽  
Hong Yao
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Hot Spot ◽  
High Temperature Superconductors ◽  
System Size ◽  
Many Body ◽  
Broken Symmetries ◽  
Sign Problem ◽  
Universal Quantum ◽  
Many Body Systems

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

scholarly journals Extensive Entropy from Unitary Evolution

2021 ◽  
Author(s):  
Yichen Huang
Keyword(s):  
Entanglement Entropy ◽  
Product State ◽  
Many Body ◽  
Unitary Evolution ◽  
Almost Everywhere ◽  
Random Product ◽  
Many Body Systems

In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

scholarly journals Diagnosing quantum chaos in many-body systems using entanglement as a resource

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Étienne Lantagne-Hurtubise ◽  
Stephan Plugge ◽  
Oguzhan Can ◽  
Marcel Franz
Keyword(s):  
Quantum Chaos ◽  
Many Body ◽  
Many Body Systems

scholarly journals Hamiltonian simulation in the low-energy subspace

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Burak Şahinoğlu ◽  
Rolando D. Somma
Keyword(s):  
System Size ◽  
High Energy ◽  
Low Energy ◽  
Many Body ◽  
Initial State ◽  
Approximation Errors ◽  
Low Energies ◽  
Hamiltonian Simulation ◽  
Many Body Systems ◽  
Product Formulas

AbstractWe study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H. This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H. We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.

scholarly journals Universal Chiral Quasisteady States in Periodically Driven Many-Body Systems

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Netanel H. Lindner ◽  
Erez Berg ◽  
Mark S. Rudner
Keyword(s):  
Many Body ◽  
Periodically Driven ◽  
Many Body Systems

scholarly journals Universality in the onset of quantum chaos in many-body systems

2021 ◽  
Vol 104 (20) ◽  
Author(s):  
Tyler LeBlond ◽  
Dries Sels ◽  
Anatoli Polkovnikov ◽  
Marcos Rigol
Keyword(s):  
Quantum Chaos ◽  
Many Body ◽  
Many Body Systems
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