scholarly journals On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
J. Hutchinson ◽  
J. P. Keating ◽  
F. Mezzadri
Keyword(s):  
Classical System ◽  
Companion Paper ◽  
Quantum Systems ◽  
Spin Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
One Dimensional ◽  
Classical Systems ◽  
Long Range Interactions ◽  
Quantum Hamiltonian

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.

scholarly journals Tunable super- and subradiant boundary states in one-dimensional atomic arrays

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Anwei Zhang ◽  
Luojia Wang ◽  
Xianfeng Chen ◽  
Vladislav V. Yakovlev ◽  
Luqi Yuan
Keyword(s):  
Long Range ◽  
Quantum States ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Metrology ◽  
One Dimensional ◽  
Topological Quantum ◽  
Long Range Interactions ◽  
Boundary States ◽  
Quantum Optical

AbstractEfficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. Recently, atomic arrays have been shown to be a promising system for exploring topological quantum optics and robust control of quantum states, where the inherent nonlinearity is included through long-range hoppings. Here we show that a one-dimensional atomic array in a periodic magnetic field exhibits characteristic properties associated with an effective two-dimensional Hofstadter-butterfly-like model. Our work points out super- and sub-radiant topological edge states localized at the boundaries of the atomic array despite featuring long-range interactions, and opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions.

One-Dimensional and Two-Dimensional Quantum Systems on Carbon Nanotube Bundles

2005 ◽  
Vol 95 (18) ◽  
Author(s):  
J. V. Pearce ◽  
M. A. Adams ◽  
O. E. Vilches ◽  
M. R. Johnson ◽  
H. R. Glyde
Keyword(s):  
Carbon Nanotube ◽  
Quantum Systems ◽  
Two Dimensional ◽  
One Dimensional ◽  
Nanotube Bundles

scholarly journals QUANTUM CORNER — TRANSFER MATRIX DMRG

2008 ◽  
Vol 19 (08) ◽  
pp. 1145-1161 ◽  
Author(s):  
ERIK BARTEL ◽  
ANDREAS SCHADSCHNEIDER
Keyword(s):  
Thermal Properties ◽  
Transfer Matrix ◽  
Heisenberg Model ◽  
Quantum Systems ◽  
Test Cases ◽  
The Novel ◽  
Simple Test ◽  
Ising Chain ◽  
One Dimensional ◽  
Classical Systems

We propose a new method for the calculation of thermodynamic properties of one-dimensional quantum systems by combining the TMRG approach with the corner transfer-matrix method. The corner transfer-matrix DMRG method brings reasonable advantage over TMRG for classical systems. We have modified the concept for the calculation of thermal properties of one-dimensional quantum systems. The novel QCTMRG algorithm is implemented and used to study two simple test cases, the classical Ising chain and the isotropic Heisenberg model. In a discussion, the advantages and challenges are illuminated.

Dark soliton dynamics for quantum systems with higher-order dispersion and higher-order nonlinearity

2021 ◽  
pp. 2150284
Author(s):  
Chen Chen ◽  
Guojun Gao ◽  
Ying Wang ◽  
Yuqi Pan ◽  
Shuyu Zhou
Keyword(s):  
Soliton Solution ◽  
Dark Soliton ◽  
Quantum Systems ◽  
Higher Order ◽  
High Order ◽  
Nonlinear Interactions ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
Order Dispersion

In this work, we investigated one-dimensional and two-dimensional quantum systems with higher-order dispersions and higher-order nonlinear interactions. Based on the high-order nonlinear Schrödinger equation (NLSE) and via the [Formula: see text]-expansion method, we derived the analytical dark soliton solution for the one-dimensional system first. By applying the self-similar method and using the results of the one-dimensional case, the analytical dark soliton solution of the system in the two-dimensional case was derived. The dynamic evolution pattern of the two-dimensional dark soliton is pictorially demonstrated. The theoretical results of our work can be used to guide the detection and experimental study of dark soliton in a two-dimensional quantum system, using high-order dispersion and higher-order nonlinear interactions.

scholarly journals Observation of parity-time symmetry breaking in a single-spin system

Science ◽  
2019 ◽  
Vol 364 (6443) ◽  
pp. 878-880 ◽  
Author(s):  
Yang Wu ◽  
Wenquan Liu ◽  
Jianpei Geng ◽  
Xingrui Song ◽  
Xiangyu Ye ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Spin Systems ◽  
Nitrogen Vacancy ◽  
Single Quantum ◽  
Single Spin ◽  
Classical Systems ◽  
Time Symmetry ◽  
Nitrogen Vacancy Center ◽  
Quantum Sensing ◽  
Vacancy Center

Steering the evolution of single spin systems is crucial for quantum computing and quantum sensing. The dynamics of quantum systems has been theoretically investigated with parity-time–symmetric Hamiltonians exhibiting exotic properties. Although parity-time symmetry has been explored in classical systems, its observation in a single quantum system remains elusive. We developed a method to dilate a general parity-time–symmetric Hamiltonian into a Hermitian one. The quantum state evolutions ranging from regions of unbroken to broken PT symmetry have been observed with a single nitrogen-vacancy center in diamond. Owing to the universality of the dilation method, our result provides a route for further exploiting and understanding the exotic properties of parity-time symmetric Hamiltonian in quantum systems.

BOSONIZATION OF TWO-DIMENSIONAL HUBBARD MODEL

1993 ◽  
Vol 07 (23) ◽  
pp. 1517-1522
Author(s):  
YU-LIANG LIU ◽  
ZHAO-BIN SU
Keyword(s):  
Hubbard Model ◽  
Charge Separation ◽  
Quantum Systems ◽  
Two Dimensional ◽  
One Dimensional ◽  
Intersection Points ◽  
1D Chains

By analyzing one-dimensional (1D) chains arranged into a two-dimensional (2D) mesh and considering electrons tunneling from chain to chain at the intersection points, we use the 1D bosonization methods to describe the 2D Hubbard model, and find that the 2D Hubbard model can be completely represented by the spin and charge fields. It may provide evidence for spin and charge separation in some 2D quantum systems.

A HAMILTONIAN FORMALISM FOR CLASSICAL SYSTEMS INTERACTING WITH QUANTUM SYSTEMS

1999 ◽  
Vol 14 (33) ◽  
pp. 2287-2302 ◽  
Author(s):  
I. ANTONIOU ◽  
E. GUNZIG ◽  
P. NARDONE ◽  
G. P. PRONKO
Keyword(s):  
Quantum System ◽  
General Framework ◽  
Classical System ◽  
Hamiltonian Formalism ◽  
Quantum Systems ◽  
Quantum Spin ◽  
Classical Particle ◽  
Quantum Oscillator ◽  
Hamiltonian Flow ◽  
Classical Systems

We propose a general framework of the combined description of a classical system with a quantum system by representing the quantum system as a Hamiltonian field and defined the evolution of the whole system as Hamiltonian flow. We illustrate the general formalism in two cases, namely the classical particle coupled with a quantum oscillator and classical particle with quantum spin in electromagnetic field.

Fourth-order constants of motion for time independent classical and quantum systems in three dimensions

2010 ◽  
Vol 88 (3) ◽  
pp. 165-174 ◽  
Author(s):  
Fakir Chand
Keyword(s):  
Hamiltonian Systems ◽  
Fourth Order ◽  
Quantum Correction ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Three Dimensions ◽  
Classical Systems ◽  
Quantum Hamiltonian ◽  
Constants Of Motion ◽  
Correction Terms

Exact fourth-order constants of motion are investigated for three-dimensional classical and quantum Hamiltonian systems. The rationalization method is utilized to obtain constants of motion for classical systems. Constants of motion for quantum systems are obtained by adding quantum correction terms, computed using Moyal's bracket, to the corresponding classical counterparts.

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