scholarly journals Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction

2009 ◽  
Vol 80 (9) ◽  
Author(s):  
Román Orús ◽  
Guifré Vidal
Keyword(s):  
Transfer Matrix ◽  
Quantum Systems ◽  
Two Dimensional ◽  
Infinite Lattice ◽  
Tensor Contraction

Neutron diffraction studies of two-dimensional quantum systems

1987 ◽  
Vol 65 (11) ◽  
pp. 1435-1439 ◽  
Author(s):  
H. J. Lauter ◽  
H. P. Schildberg ◽  
H. Godfrin ◽  
H. Wiechert ◽  
R. Haensel
Keyword(s):  
Neutron Diffraction ◽  
Domain Wall ◽  
Quantum Systems ◽  
Incommensurate Phase ◽  
Two Dimensional

The phases of D2 monolayers on graphite between the commensurate and the incommensurate phase have been investigated by neutron diffraction, revealing new features including domain-wall constructions. For the related systems, 3He and 4He adsorbed on graphite, the structure of the solid first and second layers and the interaction between them have been analyzed.

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

Decoherence in two-dimensional quantum walks with two- and four-state coins

2021 ◽  
Author(s):  
Yu-Guang Yang ◽  
Xi-Xi Wang ◽  
Jian Li ◽  
Dan Li ◽  
Yi-Hua Zhou ◽  
...  
Keyword(s):  
Quantum Correlation ◽  
Quantum Systems ◽  
Quantum Walks ◽  
Two Dimensional ◽  
Link Type ◽  
Experimental Implementation ◽  
Spatial Dimensions

Two-dimensional quantum walks using a two-state coin have simpler experimental implementation than two-dimensional quantum walks using a four-state coin. However, decoherence occurs inevitably during the evolution of quantum walks due to the coupling between the quantum systems and their environment. Thus, it is interesting to investigate the robustness against decoherence for two- and four-state two-dimensional quantum walks. Here, we investigate the effects of the decoherence on two- and four-state two-dimensional quantum walks produced by the broken-link-type noise and compare their robustness against the broken-link-type noise. Specifically, we analyze the quantum correlation between the two spatial dimensions x and y by using measurement-induced disturbance for the two-state quantum walks, i.e. the alternate walk and the Pauli walk, and the four-state quantum walks, i.e. the Grover, Hadamard and Fourier walks, respectively. Our analysis shows that the two-state walks are more robust against the broken-link-type noise than the four-state walks.

Transfer Matrix of the Two-dimensional Ising Model

2020 ◽  
pp. 211-234
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Transfer Matrix ◽  
Functional Equations ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
R Matrix ◽  
Transfer Matrix Formalism ◽  
Lowest Eigenvalue

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

scholarly journals Irrational Versus Rational Charge and Statistics in Two-Dimensional Quantum Systems

2008 ◽  
Vol 100 (11) ◽  
Author(s):  
Claudio Chamon ◽  
Chang-Yu Hou ◽  
Roman Jackiw ◽  
Christopher Mudry ◽  
So-Young Pi ◽  
...  
Keyword(s):  
Quantum Systems ◽  
Two Dimensional
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