Particle lattice models and the dynamical instability of many-body systems

1975 ◽  
Vol 44 (2) ◽  
pp. 165-168 ◽  
Author(s):  
Charles Radin
Keyword(s):  
Lattice Models ◽  
Dynamical Instability ◽  
Many Body ◽  
Many Body Systems

scholarly journals Quantum scrambling and state dependence of the butterfly velocity

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Xizhi Han ◽  
Sean Hartnoll
Keyword(s):  
High Temperature ◽  
Energy Gap ◽  
Lattice Models ◽  
State Dependence ◽  
Many Body ◽  
Ising Spin ◽  
Local Quantum ◽  
Local Lattice ◽  
Many Body Systems ◽  
Mixed Field

Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence of the out-of-time-ordered correlator in local lattice models. We verify this bound in simulations of the thermal mixed-field Ising spin chain. For scrambling operators, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap.

scholarly journals Universal quantum Hamiltonians

2018 ◽  
Vol 115 (38) ◽  
pp. 9497-9502 ◽  
Author(s):  
Toby S. Cubitt ◽  
Ashley Montanaro ◽  
Stephen Piddock
Keyword(s):  
Lattice Models ◽  
Body System ◽  
Many Body ◽  
Diverse Range ◽  
Spin Lattice ◽  
Universal Quantum ◽  
Hamiltonian Simulation ◽  
Many Body Systems ◽  
Physical Phenomena ◽  
Practical Field

Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. However, we prove that the entire physics of any quantum many-body system can be replicated by certain simple, “universal” spin-lattice models. We first characterize precisely what it means for one quantum system to simulate the entire physics of another. We then fully classify the simulation power of all two-qubit interactions, thereby proving that certain simple models can simulate all others, and hence are universal. Our results put the practical field of analogue Hamiltonian simulation on a rigorous footing and take a step toward justifying why error correction may not be required for this application of quantum information technology.

scholarly journals ORDER, DISORDER AND PHASE TRANSITIONS IN QUANTUM MANY BODY SYSTEMS

2020 ◽  
Author(s):  
Alessandro Giuliani
Keyword(s):  
Quantum Statistical Mechanics ◽  
Lattice Models ◽  
Theoretical Physics ◽  
Electron Interaction ◽  
Many Body ◽  
Many Body Theory ◽  
Decay Properties ◽  
Condensed Matter Theory ◽  
Interacting Electrons ◽  
Many Body Systems

In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on the universality of transport coecients in lattice models of interacting electrons, with specic focus on the in- dependence of the quantum Hall conductivity from the electron-electron interaction. In this context, the exchange of ideas between mathematical and theoretical physics proved particu- larly fruitful, and helped in clarifying the role played by quantum conservation laws (Ward Identities), together with the decay properties of the Euclidean current-current correlation functions, on the interaction-independence of the conductivity. 

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems

scholarly journals Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

2020 ◽  
Vol 125 (26) ◽  
Author(s):  
Norifumi Matsumoto ◽  
Kohei Kawabata ◽  
Yuto Ashida ◽  
Shunsuke Furukawa ◽  
Masahito Ueda
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Many Body ◽  
Continuous Phase Transition ◽  
Many Body Systems ◽  
Gap Closing

scholarly journals Universal relations for ultracold reactive molecules

2020 ◽  
Vol 6 (51) ◽  
pp. eabd4699
Author(s):  
Mingyuan He ◽  
Chenwei Lv ◽  
Hai-Qing Lin ◽  
Qi Zhou
Keyword(s):  
Critical Role ◽  
Interaction Strength ◽  
Quantum Correlations ◽  
Polar Molecules ◽  
Many Body ◽  
Density Correlation ◽  
Ultracold Polar Molecules ◽  
Unexplored Area ◽  
Many Body Systems

The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.

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