scholarly journals Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes

2019 ◽  
Vol 99 (15) ◽  
Author(s):  
Yunqin Zheng ◽  
Huan He ◽  
Nicolas Regnault ◽  
B. Andrei Bernevig
Keyword(s):  
Matrix Product ◽  
Restricted Boltzmann Machines ◽  
One Dimensional ◽  
Boltzmann Machines ◽  
Matrix Product States ◽  
Stabilizer Codes

scholarly journals A systematic interpolatory method for an impurity in a one-dimensional fermionic background

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Erik Jonathan Lindgren ◽  
Rafael Barfknecht ◽  
Nikolaj Zinner
Keyword(s):  
Numerical Method ◽  
Quantum Systems ◽  
Trapping Potential ◽  
Matrix Product ◽  
Contact Potential ◽  
One Dimensional ◽  
Matrix Product States ◽  
Distinguishable Particle ◽  
Analytical Result ◽  
Infinite Repulsion

We explore a new numerical method for studying one-dimensional quantum systems in a trapping potential. We focus on the setup of an impurity in a fermionic background, where a single distinguishable particle interacts through a contact potential with a number of identical fermions. We can accurately describe this system, for various particle numbers, different trapping potentials and arbitrary finite repulsion, by constructing a truncated basis containing states at both zero and infinite repulsion. The results are compared with matrix product states methods and with the analytical result for two particles in a harmonic well.

scholarly journals Tangent-space methods for uniform matrix product states

2019 ◽  
Author(s):  
Laurens Vanderstraeten ◽  
Jutho Haegeman ◽  
Frank Verstraete
Keyword(s):  
Tangent Space ◽  
Field Theories ◽  
Matrix Product ◽  
Transfer Matrices ◽  
One Dimensional ◽  
Matrix Product States ◽  
Model Hamiltonian ◽  
Different Types ◽  
Space Formalism ◽  
New Applications

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of observables, and discuss the concept of a tangent space. We explain how to variationally optimize ground-state approximations, implement real-time evolution and describe elementary excitations for a given model Hamiltonian. Also, we explain how matrix product states approximate fixed points of one-dimensional transfer matrices. We show how all these methods can be translated to the language of continuous matrix product states for one-dimensional field theories. We conclude with some extensions of the tangent-space formalism and with an outlook to new applications.

scholarly journals Fermionic matrix product states and one-dimensional topological phases

2017 ◽  
Vol 95 (7) ◽  
Author(s):  
Nick Bultinck ◽  
Dominic J. Williamson ◽  
Jutho Haegeman ◽  
Frank Verstraete
Keyword(s):  
Matrix Product ◽  
Topological Phases ◽  
One Dimensional ◽  
Matrix Product States
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