Many-particle localization

The Vielteilchenlokalisierung describes a dynamic process of an insulated multi-particle quantum system . A built-in disorder can prevent the system from thermalizing . The many-particle localization differs from the Anderson localization in the interaction of the individual particles with one another.

A general Hamilton operator for many-body localization does not exist. The phenomenon can be observed in many different models. An example of such a system, the dynamics of which is described by many-body localization, is the Heisenberg model with built-in disorder:

{\ displaystyle H _ {\ text {general Heis}} = - \ sum _ {\ langle i, j \ rangle} \ left (J ^ {x} S_ {i} ^ {x} S_ {j} ^ {x} + J ^ {y} S_ {i } ^ {y} S_ {j} ^ {y} + J ^ {z} S_ {i} ^ {z} S_ {j} ^ {z} \ right) + \ eta _ {i} S_ {i} ^ {z} \ qquad {\ text {with}} i, j \; \ mathrm {n {\ ddot {a}} next} {\ text {neighbors}}}

In addition to the generalized Heisenberg model, a random potential with the strength at each spin location is added here. lies in the interval . A quantum phase transition can be observed here from a critical size of the disorder . For small ones the system thermalizes, for large ones it localizes. ${\ displaystyle \ eta _ {i}}$ ${\ displaystyle \ eta _ {i}}$ ${\ displaystyle [-W, W]}$ ${\ displaystyle W}$ ${\ displaystyle W}$ ${\ displaystyle W}$

properties

Thermalizing quantum systems are described by the Eigenstate Thermalization Hypothesis (ETH). A thermalizing system loses all information about the initial state over long periods of time, all measurable operators approach their thermalized sizes. In contrast, in a localized system, information about the initial state persists forever. Further characteristics of many-body localization are:

The entropy of entanglement scales with the size of the interface. The entropy of entanglement grows logarithmically over time .
The conductivity of the system disappears in the localized phase.

Experimental evidence

The phenomenon of many-particle localization has already been observed in experiments with ion traps and ultra-cold atoms.

Individual evidence

↑ DM Basko, IL Aleiner, BL Altshuler: Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states . In: Annals of Physics . tape 321 , no. 5 , May 23, 2006, p. 1126–1205 , doi : 10.1016 / j.aop.2005.11.014 , arxiv : cond-mat / 0506617 .
↑ Maksym Serbyn, Z. Papić, Dmitry A. Abanin: Universal slow growth of entanglement in interacting strongly disordered systems . In: Physical Review Letters . tape 110 , no. 26 , June 28, 2013, ISSN 0031-9007 , p. 260601 , doi : 10.1103 / PhysRevLett.110.260601 , arxiv : 1304.4605 .
↑ Jens H. Bárðarson, Frank Pollmann, Joel E. Moore: Unbounded growth of entanglement in models of many-body localization . In: Physical Review Letters . tape 109 , no. 1 , July 3, 2012, ISSN 0031-9007 , p. 017202 , doi : 10.1103 / PhysRevLett.109.017202 , arxiv : 1202.5532 [abs] .
↑ DM Basko, IL Aleiner, BL Altshuler: Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states . In: Annals of Physics . tape 321 , no. 5 , May 23, 2006, p. 1126–1205 , doi : 10.1016 / j.aop.2005.11.014 , arxiv : cond-mat / 0506617 .
↑ Michael Schreiber, Sean S. Hodgman, Pranjal Bordia, Henrik P. Lüschen, Mark H. Fischer: Observation of many-body localization of interacting fermions in a quasi-random optical lattice . In: Science . tape 349 , no. 6250 , August 21, 2015, ISSN 0036-8075 , p. 842–845 , doi : 10.1126 / science.aaa7432 , arxiv : 1501.05661 .

[1] DM Basko, IL Aleiner, BL Altshuler: Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states . In: Annals of Physics . tape 321 , no. 5 , May 23, 2006, p. 1126–1205 , doi : 10.1016 / j.aop.2005.11.014 , arxiv : cond-mat / 0506617 .

[2] Maksym Serbyn, Z. Papić, Dmitry A. Abanin: Universal slow growth of entanglement in interacting strongly disordered systems . In: Physical Review Letters . tape 110 , no. 26 , June 28, 2013, ISSN 0031-9007 , p. 260601 , doi : 10.1103 / PhysRevLett.110.260601 , arxiv : 1304.4605 .

[3] Jens H. Bárðarson, Frank Pollmann, Joel E. Moore: Unbounded growth of entanglement in models of many-body localization . In: Physical Review Letters . tape 109 , no. 1 , July 3, 2012, ISSN 0031-9007 , p. 017202 , doi : 10.1103 / PhysRevLett.109.017202 , arxiv : 1202.5532 [abs] .

[4] DM Basko, IL Aleiner, BL Altshuler: Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states . In: Annals of Physics . tape 321 , no. 5 , May 23, 2006, p. 1126–1205 , doi : 10.1016 / j.aop.2005.11.014 , arxiv : cond-mat / 0506617 .

[5] Michael Schreiber, Sean S. Hodgman, Pranjal Bordia, Henrik P. Lüschen, Mark H. Fischer: Observation of many-body localization of interacting fermions in a quasi-random optical lattice . In: Science . tape 349 , no. 6250 , August 21, 2015, ISSN 0036-8075 , p. 842–845 , doi : 10.1126 / science.aaa7432 , arxiv : 1501.05661 .