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 Droplet tilings for rapid exploration of spatially constrained many-body systems

2021 ◽  
Vol 118 (34) ◽  
pp. e2020014118
Author(s):  
Anton Molina ◽  
Shailabh Kumar ◽  
Stefan Karpitschka ◽  
Manu Prakash
Keyword(s):  
Degrees Of Freedom ◽  
Experimental System ◽  
High Energy ◽  
Geometric Constraints ◽  
Material Behavior ◽  
Two Dimensional ◽  
Many Body ◽  
Lattice Systems ◽  
Initial State ◽  
Many Body Systems

Geometry in materials is a key concept which can determine material behavior in ordering, frustration, and fragmentation. More specifically, the behavior of interacting degrees of freedom subject to arbitrary geometric constraints has the potential to be used for engineering materials with exotic phase behavior. While advances in lithography have allowed for an experimental exploration of geometry on ordering that has no precedent in nature, many of these methods are low throughput or the underlying dynamics remain difficult to observe directly. Here, we introduce an experimental system that enables the study of interacting many-body dynamics by exploiting the physics of multidroplet evaporation subject to two-dimensional spatial constraints. We find that a high-energy initial state of this system settles into frustrated, metastable states with relaxation on two timescales. We understand this process using a minimal dynamical model that simulates the overdamped dynamics of motile droplets by identifying the force exerted on a given droplet as being proportional to the two-dimensional vapor gradients established by its neighbors. Finally, we demonstrate the flexibility of this platform by presenting experimental realizations of droplet−lattice systems representing different spin degrees of freedom and lattice geometries. Our platform enables a rapid and low-cost means to directly visualize dynamics associated with complex many-body systems interacting via long-range interactions. More generally, this platform opens up the rich design space between geometry and interactions for rapid exploration with minimal resources.

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

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 Quantum echo dynamics in the Sherrington-Kirkpatrick model

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Silvia Pappalardi ◽  
Anatoli Polkovnikov ◽  
Alessandro Silva
Keyword(s):  
Quantum Physics ◽  
Transverse Field ◽  
Many Body ◽  
Initial State ◽  
Large N ◽  
Semiclassical Dynamics ◽  
Long Time ◽  
Kirkpatrick Model ◽  
Ehrenfest Time ◽  
Many Body Systems

Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-N) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins N. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on N and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.

scholarly journals SO(10) grand unification in light of recent LHC searches and colored scalars at the TeV-scale

2016 ◽  
Vol 31 (08) ◽  
pp. 1650034 ◽  
Author(s):  
Ufuk Aydemir
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Gauge Coupling ◽  
High Energy ◽  
Low Energy ◽  
Grand Unification ◽  
Renormalization Group Analysis ◽  
Low Energies ◽  
Light Color ◽  
Extended Survival

We analyze the compatibility of the recent LHC signals and the TeV-scale left–right model(s) in the minimal nonsupersymmetric SO(10) framework. We show that the models in which the Higgs content is selected based on the extended survival hypothesis do not allow the [Formula: see text] boson to be at the TeV-scale. By relaxing this conjecture, we investigate various scenarios where a number of colored-scalars, originated from various Pati–Salam multiplets, are light and whence they survive down to the low energies. Performing a detailed renormalization group analysis with various low-energy Higgs configurations and symmetry breaking chains, while keeping the high energy Higgs content unmodified; we find that, among a number of possibilities, the models which have a light color-triplet scalar, and its combination with a light color-sextet, particularly stand out. Although these models do allow a TeV-scale [Formula: see text] boson, generating the required value of the gauge coupling [Formula: see text] at this scale is nontrivial.

scholarly journals Suppression of electroweak instanton processes in high-energy collisions

2021 ◽  
pp. 2150032
Author(s):  
Valentin V. Khoze ◽  
Daniel L. Milne
Keyword(s):  
Cross Section ◽  
Production Cross ◽  
High Energy ◽  
Optical Theorem ◽  
Initial State ◽  
The Past ◽  
The Standard Model ◽  
Low Energies ◽  
High Energy Collisions ◽  
High Energy Regime

Electroweak instantons are a prediction of the Standard Model and have been studied in great detail in the past although they have not been observed. Earlier calculations of the instanton production cross-section at colliders revealed that it was exponentially suppressed at low energies, but may grow large at energies (much) above the sphaleron mass. Such calculations faced difficulty in the breakdown of the instanton perturbation theory in the high-energy regime. In this paper, we review the calculation for the electroweak instanton cross-section using the optical theorem, including quantum effects arising from interactions in the initial state and show that this leads to an exponential suppression of the cross-section at all energies, rendering the process unobservable.

scholarly journals Anharmonicity-induced criticality of collective excitation in a trapped Bose–Einstein condensate

2018 ◽  
Vol 32 (31) ◽  
pp. 1850345
Author(s):  
Qun Wang ◽  
Bo Xiong
Keyword(s):  
Collective Mode ◽  
Collective Excitation ◽  
Einstein Condensate ◽  
Low Energy ◽  
Many Body ◽  
Bose Einstein Condensate ◽  
Large Numbers ◽  
Many Body Systems ◽  
Repulsive Forces ◽  
Bose Einstein

We investigate the low-energy excitations of a dilute atomic Bose gas confined in a anharmonic trap interacting with repulsive forces. The dispersion law of both surface and compression modes is derived and analyzed for large numbers of atoms in the trap, which show two branches of excitation and appear two critical values, where one of them indicates collective excitation which would be unstable dynamically, and the other one indicates the existing collective mode with lower frequency under anharmonic influence than that in harmonic trapping case. Our work reveals the key role played by the anharmonicity and interatomic forces which introduce a rich structure in the dynamic behavior of these new many-body systems.

scholarly journals Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sebastian Scherg ◽  
Thomas Kohlert ◽  
Pablo Sala ◽  
Frank Pollmann ◽  
Bharath Hebbe Madhusudhana ◽  
...  
Keyword(s):  
Density Wave ◽  
Many Body ◽  
Initial State ◽  
Free System ◽  
One Dimensional ◽  
Ergodic Behavior ◽  
Wide Range ◽  
Clean System ◽  
Initial Charge ◽  
Many Body Systems

AbstractThe thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.

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