Disordered systems t=10000 spin glass Tensor network approaches to - PowerPoint PPT Presentation

Disordered systems t=10000 ✤ spin glass Tensor network approaches to 
 ✤ high-T superconductor Disordered quantum systems ✤ Anderson localization t=10000 ✤ many-body localization Yu-Cheng Lin / National Chengchi University ✤ disorder-induced spin liquid December, 2018 @ RIKEN-CCS, Kobe


 Numerical challenges Heisenberg chain X S i · ~ ~ ✤ long relaxation time (clean chain) H = J S i +1 i ✤ tendency to get stuck in local minima spin-spin correlations at T=0 S i + r i ⇠ ln 1 / 2 ( r ) ✤ disorder average C ( r ) = ( � 1) r h ~ S i · ~ r entanglement entropy ✤ broken translational invariance (iDMRG) S ∞ ( ` ) = 1 3 log 2 ` + c 1 ✤ difficult even in 1D `


 Strong-disorder RG 
 Disordered Heisenberg chain Ma, Dasgupta, Hu(1979) 
 (SDRG) Dasgupta, Ma (1980) 
 D. Fisher, (1994) ✤ Project the strongest coupled pair of spins to singlet (random chain) X J i ~ S i · ~ H = S i +1 strongest coupling Ω i ✤ mean spin-spin correlation at T=0 
 C ( r ) ∼ 1 1 p 2 ( | "#i � | #"i ) r 2 J = JJ 0 effective coupling ˜ 2 Ω < Ω ✤ mean entanglement entropy 
 D. Fisher (1995) S ∞ ( ` ) = ln 2 Refael & Moore (2004) 3 log 2 ` + c 1 ` Random-singlet state: a non-crossing valence-bond state