Moscow Institute of Physics and Technology

Theoretical nanophysics laboratory (laboratory is closed since 31.12.2016)

Upcoming seminars
colloquium, Friday, April 5, 2019, , 11:30 am

Vladimir Kravtsov

Correlation-induced localization

Conventional Anderson localization is due to destructive interference of matter waves described by local random Hamiltonians. Correlations in random diagonal elements of such a Hamiltonian are known to favor delocalization. Recently systems with non-local Hamiltonians become experimentally accessible. We consider two families of such random matrix Hamiltonians with correlations in the long-range hopping terms and demonstrate that localization is enhanced and the wave function ergodicity is progressively degrading as the correlations become stronger.

We review the localization/delocalization criteria of Mott and Anderson and show that the former is the sufficient criterion of weak ergodicity and the latter is the sufficient criterion of localization. The fact that these two criteria are not complimentary is the reason why the non-ergodic extended (multifractal) states may exist when neither the Mott, nor the Anderson criterion is fulfilled.
We suggest a new class of random matrix models (Toeplitz RMT) with translation-invariant hopping integrals and identify the character of eigenfunction and eigenvalue statistics in them. We formulate the principles of level statistics if the type of eigenfunction statistics is known both in the coordinate and in the momentum basis and demonstrate that for the Toeplitz RMT the ergodic delocalization in the coordinate space may coexist with the Poisson level statistics.
Finally, we suggest a matrix-inversion trick that allows to identify uniquely the type of eigenfunction statistics and prove the absence of delocalized states in the bulk of spectrum of long-range Hamiltonians with deterministic (fully correlated) hopping.

Visiting address:

Laboratory building, room 122
Moscow Institute of Physics and Technology
Dolgoprudny, Russia

contact e-mail address: nanotheory@phystech.edu (head M.V.Feigel'man, deputy head I.V.Zagorodnev)

Research topics
  • Mesoscopic electronic systems
  • Superconducting hybrid structures
  • Quantum phase transitions
  • Spintronics
  • 2DEG and quantum Hall effect
  • Quantum magnetism and topological order
  • Physics of quantum computation
Recent quantum-nanophysics seminars
Scientific Council of the Landau Institute, Friday, March 22, 2019, Landau Institute, 11:30 am

A.Ya. Maltsev

Obshchie osobennosti uglovykh diagramm provodimosti metallov v sil'nykh magnitnykh polyakh i slozhnost' uglovykh diagrammakh magnitoprovodimosti v sil'nykh magnitnykh polyakh

My rassmotrim samye obshchie osobennosti uglovykh diagramm provodimosti v normal'nykh metallakh so slozhnymi poverkhnostyami Fermi v prisutstvii sil'nykh magnitnykh polei. Opisanie takikh osobennostei budet osnovano na topologicheskom opisanii dinamicheskoi sistemy, voznikayushchei dlya evolyutsii elektronnykh sostoyanii na poverkhnosti Fermi v prisutstvii vneshnego magnitnogo polya. My rassmotrim uglovye diagrammy provodimosti dlya normal'nykh (monokristallicheskikh) metallov so slozhnymi poverkhnostyami Fermi v prisutstvii sil'nykh magnitnykh polei. Povedenie provodimosti v etom sluchae sil'no zavisit ot napravleniya magnitnogo polya i ustoichivye netrivial'nye rezhimy takogo povedeniya sootvetstvuyut pri etom spetsial'nym zonam ustoichivosti na uglovoi diagramme, otvechayushchim opredelennym (topologicheskim) svoistvam tenzora provodimosti. Kak my pokazhem, v obshchem sluchae mozhno razdelit' takie diagrammy na dva obshchikh tipa, prostye (tip A) i slozhnye (tip B). Nas budut interesovat' pri etom diagrammy vtorogo tipa, obladayushchie ryadom spetsificheskikh osobennostei (beskonechnoe chislo zon ustoichivosti, nalichie khaoticheskikh rezhimov i t.p.), kotorye my rassmotrim bolee podrobno. Po rezul'tatam rabot: ZhETF, t. 151, vyp. 5, 944-973 (2017); ZhETF, t. 152, vyp. 5(11), 1053-1064 (2017) , ZhETF, 154(6), 1183-1210 (2018)

Scientific Council of the Landau Institute, Friday, March 22, 2019, Landau Institute, 11:30 am

A.Ya. Maltsev, S.P. Novikov

Ergodic properties of dynamic systems on two-dimensional surfaces and electron transport phenomena in normal metals

V doklade obsuzhdaetsya svyaz' spetsial'nykh kharakteristik dinamicheskikh sistem na poverkhnostyakh (indeksov Zoricha - Kontsevicha - Forni) s povedeniem provodimosti v metallakh v sil'nykh magnitnykh polyakh. Dannoe rassmotrenie yavlyaetsya vazhnym v sluchae vozniknoveniya naibolee slozhnykh (khaoticheskikh) elektronnykh traektorii na poverkhnosti Fermi, vozmozhnom dlya dostatochno slozhnykh poverkhnostei i spetsial'nykh napravlenii magnitnogo polya. Kak mozhno pokazat', upomyanutye kharakteristiki imeyut neposredstvennoe otnoshenie k povedeniyu magnitoprovodimosti, takim obrazom, mozhno v printsipe govorit' o vozmozhnosti ikh eksperimental'nogo opredeleniya v sootvetstvuyushchikh sluchayakh. Po rezul'tatam raboty: Trudy MIAN, tom 302, (2018) str. 296–315

Department of quantum mesoscopics: seminar, Friday, March 15, 2019, ITF, 3:00 pm

A.V. Lunkin

Geometricheskii podkhod k resheniyu SYK

(po motivam izucheniya stat'i A.Yu. Kitaeva)

Scientific Council of the Landau Institute, Friday, March 15, 2019, Landau Institute, 11:30 am

A.V. Lunkin, K.S. Tikhonov, M.V. Feigel'man

SYK model with quadratic perturbations: the route to a non-Fermi-liquid

Model' SYK (Sachedev-Ye-Kitaev) opisyvaet sistemu sluchaino vzaimodeistvuyushchikh maioranovskikh fermionov bez kvadratichnykh chlenov v gamil'toniane. V predele bol'shogo chisla fermionov (N) i nizkikh temperaturakh (T « J, gde J - kharakternyi masshtab vzaimodeistviya) funktsiya Grina modeli, v sedlovom priblizhenii, imeet ne fermi-zhidkostnoe povedenie G(t) ~ t^(-1/2). Odnako, sedlovye uravneniya obladayut vysokoi simmetriei i dopuskayut zamenu t na proizvol'nuyu monotonnuyu funktsiyu f(t). Takoe reshenie imeet tol'ko SL(2,R) simmetriyu. Ponizhenie simmetrii ot polnoi gruppy reparametrizatsii do SL(2,R) privodit k sushchestovaniyu myagkoi mody, kotoraya stanovitsya sushchestvenna pri NT « J . Funktsiya Grina na samykh bol'shikh vremenakh menyaet svoyu asimptotiku na G(t) ~ t^(-3/2).
V nashei rabote my issleduem vliyanie kvadratichnogo vozmushcheniya na eto povedenie. Naivnoe rassmotrenie sedlovykh uravnenie pokazyvaet, chto na bol'shikh vremenakh fermi-zhidkostnoe povedenie dolzhno vosstanavlivat'sya. Odnako, voznikaet vopros: chto, proizoidet esli eti vremena budut stol' bol'shimi, chto nuzhno uchityvat' fluktuatsii myagkoi mody? Rassmatrivaya vtoroi poryadok teorii vozmushcheniya my pokazyvaem, chto sushchestvuet nenulevoi interval amplitud vozmushchenii, kogda povedenie funktsii Grina ne menyaetsya, sokhranyaya asimptotiku G(t) ~ t^(-3/2). Eto pozvolyaet nadeyat'sya na ispol'zovanie modeli SYK dlya postroeniya kontroliruemoi teorii ne-fermizhidkostnogo povedeniya sil'no vzaimodeistvuyushchikh fermionov.