Transfer-matrix density-matrix renormalization-group theory for thermodynamics of one-dimensional quantum systems

1997 ◽  
Vol 56 (9) ◽  
pp. 5061-5064 ◽  
Author(s):  
Xiaoqun Wang ◽  
Tao Xiang
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Density Matrix ◽  
Transfer Matrix ◽  
Quantum Systems ◽  
Density Matrix Renormalization Group ◽  
Renormalization Group Theory ◽  
One Dimensional ◽  
Matrix Density ◽  
Density Matrix Renormalization

DENSITY MATRIX RENORMALIZATION GROUP: INTRODUCTION FROM A VARIATIONAL POINT OF VIEW

1999 ◽  
Vol 13 (01) ◽  
pp. 1-24 ◽  
Author(s):  
T. NISHINO ◽  
T. HIKIHARA ◽  
K. OKUNISHI ◽  
Y. HIEIDA
Keyword(s):  
Renormalization Group ◽  
Group Theory ◽  
Variational Method ◽  
Density Matrix ◽  
Point Of View ◽  
Density Matrix Renormalization Group ◽  
Renormalization Group Theory ◽  
Future Directions ◽  
Density Matrix Renormalization ◽  
Recent Developments

The density matrix renormalization group theory is reviewed as a numerical variational method. The variational state, expressed as a product of local tensors, is improved through locally tuning each tensor. The first section is a tutorial with simplified discussions. Details are discussed in the subsequent sections. The review concludes with some recent developments and future directions.

RECENT PROGRESS IN THE DENSITY-MATRIX RENORMALIZATION GROUP

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2564-2575 ◽  
Author(s):  
ULRICH SCHOLLWÖCK
Keyword(s):  
Renormalization Group ◽  
Density Matrix ◽  
Quantum Systems ◽  
Density Matrix Renormalization Group ◽  
Strongly Correlated ◽  
Powerful Method ◽  
Numerical Renormalization Group ◽  
One Dimensional ◽  
Density Matrix Renormalization ◽  
Quantum Impurity

Over the last decade, the density-matrix renormalization group (DMRG) has emerged as the most powerful method for the simulation of strongly correlated one-dimensional (1D) quantum systems. Input from quantum information has allowed to trace the method's performance to the entanglement properties of quantum states, revealing why it works so well in 1D and not so well in 2D; it has allowed to devise algorithms for time-dependent quantum systems and, by clarifying the link between DMRG and Wilson's numerical renormalization group (NRG), for quantum impurity systems.

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