Simulating strongly correlated systems with fermionic alkaline earth atom isotops in optical lattices and related quantum chemistry of transition metal complexes  Page description

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Details of project

  
Identifier
100908
Type K
Principal investigator Legeza, Örs
Title in Hungarian Erősen korrelált rendszerek szimulációja fermionos alkáli föld atom izotópokkal optikai rácsokon és az átmeneti-fémek kapcsolódó kvantumkémiája
Title in English Simulating strongly correlated systems with fermionic alkaline earth atom isotops in optical lattices and related quantum chemistry of transition metal complexes
Keywords in Hungarian szilárdtestfizika, kvantumkémia, kvantuminformáció-elmélet, DMRG, TNS, optikai rácsok, nanostruktúrák,polidiacetilének
Keywords in English condensed matter, quantum chemistry, quantum information theory, DMRG, TNS, ultra cold atoms, nanostructures, polydiacetylenes
Discipline
Solid-state Physics (Council of Physical Sciences)50 %
Ortelius classification: Solid state physics
Analytical Chemistry (Council of Physical Sciences)25 %
Ortelius classification: Analytical chemistry
Information Technology (Council of Physical Sciences)25 %
Ortelius classification: Applied informatics
Panel Physics 1
Department or equivalent Theoretical Solid State Physics Department (Wigner Research Centre for Physics)
Participants Barcza, Gergely
Hagymási, Imre
Sólyom, Jeno
Szalay, Szilárd
Szirmai, Edina
Woynarovich, Ferenc
Starting date 2012-01-01
Closing date 2015-12-31
Funding (in million HUF) 18.836
FTE (full time equivalent) 16.70
state closed project
Summary in Hungarian
Az elmúlt néhány évben, a fermion jellegű alkáliföldatom izotópok rendkívül egyedi tulajdonságainak köszönhetően az optikai rácsokon megvalósítható erősen korrelált rendszerek ugrásszerű fejlődésen mentek keresztül.
A kialakuló rendkívül magas SU(N) (2<= N <= 10) szimmetria számos olyan új fizikai összefüggés tanulmányozását teszi lehetővé, melynek analógiája nem ismert a kondenzált anyagok körében, sőt a kvantumos információ manipulálását célzó rendszerek kutatásához is nagyban hozzájárul. Többek között új eredmények várhatók az átmentifém-oxidok, nehéz fermion és spin-folyadék fázisok esetében. Az átmentifém-vegyületek igen érdekes kémiája pedig éppen a kvantumkémia egyik legnagyobb kihívása a komplikált elektronszerkezet, a relativisztikus effektusok felerősödése és a reakciókban megjelenő közbenső állapotok révén. A kvantuminformáció-elmélet számos koncepcióját magába foglaló sűrűségmátrixos renormálásicsoport (DMRG) algoritmus mindkét területen megfelelő elméleti megközelítést biztosít, sőt napjainkban a számítógépes erőforrások gyors ütemű fejlődésének köszönhetően már a kísérleti eredmények egy jelentős részének reprodukálására is lehetőség nyílt. Az erősen korrelált rendszerek ún. összefonódottsági topológiáját jobban tükröző tenzorhálózat-állapot (TNS) alapú algoritmusok kifejlesztésétől pedig az elméleti fizika a magasabb dimenziókban lejátszódó folyamatok szimulációját és megértését várja. Mindez a nanotechnológiában fontos szerepet betöltő polidiacetilének tulajdonságának pontosabb meghatározását, illetve a kétdimenziós grafénben a kölcsönhatások leírását is lehetővé teszi.
A jelen pályázat keretében a fentiekben vázolt rendszerek tulajdonságait kívánjuk meghatározni analitikus és numerikus módszerek segítségével, illetve a kvantuminformáció-elmélet számos koncepcióját kihsználva új numerikus renormálási algoritmust kifejleszteni.
Summary
In the last few years strongly correlated systems that can be realized with ultracold atoms loaded into optical lattices became the focus of interest. One of the most important reasons behind this is special unique feature of fermionic alkali earth metal isotopes. These systems can have extremely high symmetry like SU(n) where 2<= n <= 10. Due to this high symmetry, it is possible to study numerous novel physical phenomena, including those that do not have analogues in condensed matter physics. Moreover, studying of these high symmetric systems gives very important contribution to the investigation of quantum information theory and quantum computation. Among others, new results can be expected on transition-metal-oxides, heavy fermion systems or spin liquids states. The transition-metal-oxides have highly unique chemical properties that are direct consequences of their complicated electronic structures, increasing relativistic effects, and appearance of different intermediate states in the chemical reactions. Due to these special properties, the investigation of transition-metal-componds rose to the biggest challenges of quantum chemistry. The density-matrix-renormalization-group (DMRG) algorithm that involve numerous concepts of quantum information theory provides adequate theoretical treatment for both research topics, namely SU(n) symmetric strongly correlated systems and quantum chemistry, respectively. Furthermore, in these days, the computational resources are developing extremely fast, and it allows to reproduce various interesting experimental results, too. Another promising way is the tensor-network-state (TNS) based algorithms which reflect more explicitly the so-called entanglement topology of strongly correlated systems. This method seems to be promising to help to understand and simulate physical processes in higher dimensions, and opens possibility e.g. to determine more precisely the properties of polydiacetylens which plays important role in nanotechnology, or to describe the different interaction processes in the two-dimensional graphene. Within the scope of the present proposal, we would like to determine the properties of the systems described above by different analytical and numerical methods and to develop new numerical renormalization algorithm exploiting various concepts of quantum information theory.




 

Final report

  
Results in Hungarian
A négyéves időszak alatt kivitelezett elméleti kutatás a kvantummechanika törvényein alapuló új matematikai algoritmusok fejlesztésére fókuszál, melyek összességükben lehetővé teszik eddigieknél bonyolultabb kvantumrendszerek szimulációját, és viselkedésük előrejelzését vagy tulajdonságaik tervezését. A kutatási terv értelmében számos erősen korrelált mágneses és elektron rendszert vizsgáltuk analitikus módszerek és numerikus megközelítések használatával. Eredményeink interdiszciplinárisak, és az Anderson és Kondo rendszerek, ultra-hideg atomi rendszerek, kvantumkémia, relativisztikus kvantumkémia, magfizika, informatika, anyagtudomány, kvantum információ elmélet, és a tenzorfaktorizáció matematikai aspektusainak területeit fedik le. Eredményeinket nemzetközi konferenciákon mutattuk be és magas presztízsű újságokban publikáltuk. Végrehajtottuk a kitűzött feladatot. Néhány részfeladatot nem tekintettünk, mivel új kutatási területek bukkantak fel, melyeket fontosabbaknak ítéltünk. Összesen 44 tudományos cikket, 5 dolgozatot, 3 online elérhető jegyzetet publikáltunk. Továbbá nagyszabású algoritmus fejlesztést kiviteleztünk, kifejlesztettük a fa-TNS algoritmust, a relativisztikus problémák kezelésére való négy-komponensû (4c-) DMRG-t, egy magfizikai alkalmazásokra optimalizált DMRG algoritmust, és a DMRG egy új hibrid CPU-GPU implementációját.
Results in English
The theoretical research, carried out during the four-year time period, is focusing on the development of new mathematical algorithms based on the laws of quantum mechanics, which altogether makes possible the simulation of quantum systems more complex than ever, and the prediction of their behavior or the designing of their properties. According to the research plan we have studied various strongly correlated magnetic and electronic systems using analytical methods and numerical approaches. Our results are highly interdisciplinary and they cover the fields of Anderson and Kondo systems, ultra-cold atoms, quantum chemistry, relativistic quantum chemistry, nuclear structure theory, computer science, material science, quantum information theory and mathematical aspects of tensor factorizations. Our results have been presented in international conferences and published in high quality journals. We have accomplished the tasks outlined in the proposal. Some partial tasks were not treated as new research areas emerged that we found to be more important. Altogether we have published some 44 scientific papers, 5 dissertations, 3 on-line accessible lecture notes. We have also carried out major algorithmic developments and developed the tree-TNS algorithm, the four-component (4c-) DMRG to deal with relativistic problems, an efficient DMRG to treat nuclear shell models, and a smart hybrid CPU-GPU implementation of the DMRG.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=100908
Decision
Yes





 

List of publications

  
Hagymási I, Itai K*, Sólyom J: Periodic Anderson model with correlated conduction electrons: Variational and exact diagonalization study, Physical Review B, 85, 235116/1-13, 2012
Hagymási I, Itai K*, Sólyom J: Periodic Anderson model with d-f interaction, Proceedings of the European Conference Physics of Magnetism 2011, Poznan, Acta Physica Polonica, 2012
Barcza G, Legeza Ö, Noack R M*, Sólyom J: On the dimerized phase in the cross-coupled antiferromagnetic spin ladder, Phys. Rev. B 86, 075133, 2012
Schneider R*, Rohwedder T*, Legeza Ö: Numerical approaches for high-dimensional PDE's for quantum chemistry, Encyclopedia of Applied and Computational Mathematics, B. Engquist edt., Springer, 2013
Barcza G, Szirmai E, Legeza Ö, Sólyom J: Emergence of Quintet Superfluidity in the Chain of Partially Polarized Spin-3/2 Ultracold Atom, Phys. Rev. A Rapid Com 86, 061602, 2012
Boguslawski K, Marti K. H., Legeza Ö, Reiher M: Accurate ab initio spin densities, J. Chem. Theory Comput. 2012, 8, 1970－1982., 2012
Boguslawski K, Tecmer P, Legeza Ö, and Reiher M: Entanglement Measures for Single- and Multi-Reference Correlation Effects, J. Phys. Chem. Lett., 2012, 3 (21), 3129-3135, 2012
Ö. Legeza, M. Reiher, B. Paulus, R. Schneider: Entanglement based approaches in quantum chemsitry (EBAQC), MPI-PKS, Dresden, 2012
Barcza G, Gebhard F, Legeza O: Rigorous treatment of strong electronic correlations in polydiacetylene chains, MOLECULAR PHYSICS 111:(16-17) pp. 2506-2515., 2013
Barcza G, Barford W, Gebhard F, Legeza O: Excited states in polydiacetylene chains: A density matrix renormalization group study, PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS 87:(24) Paper 245116. 16 p., 2013
Boguslawski K, Tecmer P, Barcza G, Legeza O, Reiher M: Orbital entanglement in bond-formation processes, JOURNAL OF CHEMICAL THEORY AND COMPUTATION 9:(7) pp. 2959-2973., 2013
Csaba Nemes, Gergely Barcza, Zoltan Nagy, Ors Legeza, Peter Szolgay: Implementation trade-offs of the density matrix renormalization group algorithm on kilo-processor architectures, In: 21st European Conference on Circuit Theory and Design DOI:10.1109/ECCTD.2013.6662251, 2013
Hagymasi I, Itai K, Solyom J: Hubbard physics in the symmetric half-filled periodic anderson-hubbard model, JOURNAL OF THE KOREAN PHYSICAL SOCIETY 62:(10) pp. 1423-1426, 2013
Hagymási I, Itai K, Sólyom J: Quantum criticality and first-order transitions in the extended periodic Anderson model, PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS 87:(12) Paper 125146. 7 p., 2013
Szalay Sz: Quantum entanglement in finite-dimensional Hilbert spaces, arXiv:1302.4654, 2013
Örs Legeza, Thorsten Rohwedder, Reinhold Schneider, Szilárd Szalay: Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry, arXiv:1310.2736 accepted for publ in "Many-Electron Approaches in Physics, Chemistry and Mathematics" by V. Bach and L. Delle Site, 2013
Timár Máte: Erősen korrelált rendszerek vizsgálata renormálási módszerekkel, BsC Thesis, 2013
Nemes Cs, Barcza G, Nagy Z, Legeza Ö, Szolgay P: The density matrix renormalization group algorithm on kilo-processor architectures: implementation and trade-offs, arXiv:1309.5571 accepted for publ in Computer Physics Communications, 2013
Stefan Knecht, Ors Legeza, Markus Reiher: Four-Component Density Matrix Renormalization Group, arXiv:1312.0970 accepted for publ in Journal of Chemical Physics, 2013
Pawel Tecmer, Katharina Boguslawski, Ors Legeza, Markus Reiher: Unravelling the quantum-entanglement effect of noble gas coordination on the spin ground state of CUO, Phys. Chem. Chem. Phys, 16, 719–727., 2014
Edina Szirmai: Two-orbital physics of high spin fermionic alkaline earth atoms confined in a one-dimensional chain, Phys. Rev. B, 88 195432, 2013
P. Sinkovicz, A. Zamora, E. Szirmai, M. Lewenstein, G. Szirmai: Spin liquid phases of alkaline-earth-metal atoms at finite temperature, Phys. Rev. A 88, 043619, 2013
Örs Legeza, Thorsten Rohwedder, Reinhold Schneider, Szilárd Szalay: Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry, arXiv:1310.2736; In: Bach V , Delle Site L Many-Electron Approaches in Physics, Chemistry and Mathematics . Heidelberg: SIP. 2014. pp 53-76 ISBN:978-3-319-06378-2, 2013
Nemes Cs, Barcza G, Nagy Z, Legeza Ö, Szolgay P: The density matrix renormalization group algorithm on kilo-processor architectures: implementation and trade-offs, arXiv:1309.5571; COMPUTER PHYSICS COMMUNICATIONS 185:(6) pp. 1570-1581. (2014), 2014
Stefan Knecht, Ors Legeza, Markus Reiher: Four-Component Density Matrix Renormalization Group, JOURNAL OF CHEMICAL PHYSICS 140:(4) Paper 041101. 5 p. (2014), 2014
Fertitta E , Paulus B , Barcza G , Legeza Ö: Investigation of metal-insulator-like transition through the ab initio density matrix renormalization group approach, PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS 90:(24) Paper 245129. (2014), 2014
Hagymasi I , Solyom J , Legeza Ö: Interorbital interaction in the one-dimensional periodic Anderson model: A density-matrix renormalization-group study, PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS 90: Paper 125137. 10 p. (2014), 2014
Magda GZs , Jin XZ , Hagymási I , Vancsó P , Osváth Z , Nemes-Incze P , Hwang CY , Biro LP , Tapasztó L: Room-temperature magnetic order on zigzag edges of narrow graphene nanoribbons, NATURE: INTERNATIONAL WEEKLY JOURNAL OF SCIENCE 514: pp. 608-611. (2014), 2014
Mottet M , Tecmer P , Boguslawski K , Legeza Ö , Reiher M: Quantum entanglement in carbon-carbon, carbon-phosphorus and silicon-silicon bonds, PHYSICAL CHEMISTRY CHEMICAL PHYSICS 16:(19) pp. 8872-8880. (2014), 2014
G. Barcza, R. M. Noack, and J. Sólyom, Ö Legeza: Entanglement patterns and generalized correlation functions in quantum many body systems, arXiv:1406.6643, submitted to JSTAT, 2014
G. Barcza, E. Szirmai, J. Sólyom, Ö. Legeza: Phase Separation of Superfluids in the Chain of Four-Component Ultracold Atoms, Accepted for publication in EPJ (2014), arXiv 1409.4867, 2015
V M.urg, F. Verstraete, R. Schneider, P. R. Nagy, O. Legeza: Tree tensor network state study of the ionic-neutral curve crossing of LiF, arXiv:1403.0981 aceepted for publication in 5JCTC, 2015
16. Corinne Duperrouzel, Paweł Tecmer, Katharina Boguslawski, Gergerly Barcza, Örs Legeza, Paul W. Ayers: A quantum informational approach for dissecting chemical reactions, Chemical Physics Letters 621:160-164. DOI: 10.1016/j.cplett.2015.01.005, 2015
17. Szilárd Szalay, Max Pfeffer, Valentin Murg , Gergely Barcza, Frank Verstraete, Reinhold Schneider, Ö. Legeza: Tensor product methods and entanglement optimization for ab initio quantum chemistry, accepted for publication in Int. Jour. Quant. Chem. arxiv:14125829, 2015
Ö. Legeza: New wavefucntion methods and entanglement optimizations in quantum chemistry, http://tagung-theoretische-chemie.uni-graz.at/en/past-workshops/workshop-2014/, Lecture Notes, 2014
Ö. Legeza: Generalized tensor methods and entanglement measurements for strongly correlated systems, http://ldqs.iyte.edu.tr/wp-content/uploads/2014/08/Legeza_izmir_2014_v01.pdf, Lecture Notes, 2014
Szalay S: Entanglement and correlations: an introduction, 4 September 2014, Budapest, Wigner FK (2014), 2014
Hagymási I: Nehézfermionos és vegyes valenciájú viselkedés kiterjesztett periodikus Anderson-modellekben, PhD Thesis 2014, 2014
E. Szirmai, and H. Nonne: Competing valence bond states of spin-3/2 fermions on strongly coupled ladder, Phys. Rev. B 90, 245135 (2014), 2014
Barcza G, Legeza Ö, Noack R M*, Sólyom J: On the dimerized phase in the cross-coupled antiferromagnetic spin ladder, Phys. Rev. B 86, 075133, 2012
Barcza G, Szirmai E, Legeza Ö, Sólyom J: Emergence of Quintet Superfluidity in the Chain of Partially Polarized Spin-3/2 Ultracold Atom, Phys. Rev. A Rapid Com 86, 061602, 2012
Boguslawski K, Marti K. H., Legeza Ö, Reiher M: Accurate ab initio spin densities, J. Chem. Theory Comput. 2012, 8, 1970－1982., 2012
Boguslawski K, Tecmer P, Legeza Ö, and Reiher M: Entanglement Measures for Single- and Multi-Reference Correlation Effects, J. Phys. Chem. Lett., 2012, 3 (21), 3129-3135, 2012
Barcza G, Gebhard F, Legeza O: Rigorous treatment of strong electronic correlations in polydiacetylene chains, MOLECULAR PHYSICS 111:(16-17) pp. 2506-2515., 2013
Barcza G, Barford W, Gebhard F, Legeza O: Excited states in polydiacetylene chains: A density matrix renormalization group study, PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS 87:(24) Paper 245116. 16 p., 2013
Boguslawski K, Tecmer P, Barcza G, Legeza O, Reiher M: Orbital entanglement in bond-formation processes, JOURNAL OF CHEMICAL THEORY AND COMPUTATION 9:(7) pp. 2959-2973., 2013
Hagymasi I, Itai K, Solyom J: Hubbard physics in the symmetric half-filled periodic anderson-hubbard model, JOURNAL OF THE KOREAN PHYSICAL SOCIETY 62:(10) pp. 1423-1426, 2013
Stefan Knecht, Ors Legeza, Markus Reiher: Four-Component Density Matrix Renormalization Group, JOURNAL OF CHEMICAL PHYSICS 140:(4) Paper 041101. 5 p. (2014), 2014
Pawel Tecmer, Katharina Boguslawski, Ors Legeza, Markus Reiher: Unravelling the quantum-entanglement effect of noble gas coordination on the spin ground state of CUO, Phys. Chem. Chem. Phys, 16, 719–727., 2014
Fertitta E , Paulus B , Barcza G , Legeza Ö: Investigation of metal-insulator-like transition through the ab initio density matrix renormalization group approach, PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS 90:(24) Paper 245129. (2014), 2014
Hagymasi I , Solyom J , Legeza Ö: Interorbital interaction in the one-dimensional periodic Anderson model: A density-matrix renormalization-group study, PHYSICAL REVIEW B CONDENSED MATTER AND MATERIALS PHYSICS 90: Paper 125137. 10 p. (2014), 2014
Magda GZs , Jin XZ , Hagymási I , Vancsó P , Osváth Z , Nemes-Incze P , Hwang CY , Biro LP , Tapasztó L: Room-temperature magnetic order on zigzag edges of narrow graphene nanoribbons, NATURE: INTERNATIONAL WEEKLY JOURNAL OF SCIENCE 514: pp. 608-611. (2014), 2014
Mottet M , Tecmer P , Boguslawski K , Legeza Ö , Reiher M: Quantum entanglement in carbon-carbon, carbon-phosphorus and silicon-silicon bonds, PHYSICAL CHEMISTRY CHEMICAL PHYSICS 16:(19) pp. 8872-8880. (2014), 2014
G. Barcza, R. M. Noack, and J. Sólyom, Ö Legeza: Entanglement patterns and generalized correlation functions in quantum many body systems, Phys. Rev. B 92, 125140 (2015), 2015
G. Barcza, E. Szirmai, J. Sólyom, Ö. Legeza: Phase Separation of Superfluids in the Chain of Four-Component Ultracold Atoms, Eur. Phys. J. ST 224: 533-538 (2015), 2015
V M.urg, F. Verstraete, R. Schneider, P. R. Nagy, O. Legeza: Tree tensor network state study of the ionic-neutral curve crossing of LiF, J. Chem. Theory Comput. 11, 1027-1036 (2015), 2015
16. Corinne Duperrouzel, Paweł Tecmer, Katharina Boguslawski, Gergerly Barcza, Örs Legeza, Paul W. Ayers: A quantum informational approach for dissecting chemical reactions, Chem. Phys. Lett. 621, 160-164 (2015), 2015
17. Szilárd Szalay, Max Pfeffer, Valentin Murg , Gergely Barcza, Frank Verstraete, Reinhold Schneider, Ö. Legeza: Tensor product methods and entanglement optimization for ab initio quantum chemistry, Int. J. Quant. Chem. \textbf{115}, 1342-1391 (2015), 2015
W. Brzezicki, I. Hagymási, J. Dziarmaga, Ö. Legeza: Second-order Peierls transition in the spin-orbital Kumar-Heisenberg model, Phys. Rev. B 91, 205137 (2015), 2015
E. Fertitta, B. Paulus, G. Barcza, Ö. Legeza: On the calculation of complete dissociation curves of closed-shell pseudo-onedimensional systems through the multireference method of increments, J. Chem. Phys. 143, 114108 (2015), 2015
G. Ehlers, J. Sólyom, Ö. Legeza, R. M. Noack: Entanglement structure of the Hubbard model in momentum space, Phys. Rev. B 92, 235116 (2015), 2015
I. Hagymási, J. Sólyom, Ö. Legeza: Competition between Hund's coupling and Kondo effect in a one-dimensional extended periodic Anderson model, Phys. Rev. B 92, 035108, (2015), 2015
I. Hagymási, J. Sólyom, Ö. Legeza: Momentum distribution functions in a one-dimensional extended periodic Anderson model, Adv. in Cond. Mat. Phys. 2015, 614017 (2015), 2015
Ö Legeza, L Veis, A Poves, J Dukelsky: Advanced density matrix renormalization group method for nuclear structure calculations, Phys. Rev. C \textbf{92}, 051303 (2015), 2015
Yilin Zhao, Katharina Boguslawski, Pawe³ Tecmer, Corinne Duperrouzel, Gergely Barcza, Örs Legeza, Paul W Ayers: Dissecting the Bond Formation Process of $d^{10}$-Metal-Ethene Complexes with Multireference Approaches, Theor. Chem. Acc. 2015, 134:120 (2015), 2015
Sz. Szalay: Multipartite entanglement measures, Phys. Rev. A 92, 042329 (2015), 2015
C. Krumnow, Ö. Legeza, J. Eisert: Fermionic orbital optimisation in tensor network states, arXiv:1504.00042 (2015) submitted to Phys. Rev. Lett, 2015
T. Szilvási, G. Barcza, Ö. Legeza: Concept of chemical bond and aromaticity based on quantum information theory, arXiv:1509.04241 submitted to JACS, 2015
M. Timár, G. Barcza, F. Gebhard, L. Veis, Ö. Legeza: Hückel--Hubbard-Ohno modeling of $\pi$-bonds in ethene and ethyne with application to trans-polyacetylene, arXiv:1512.03229 submitted to PCCP, 2015
E. Szirmai, G. Barcza, J. Sólyom, Ö. Legeza: Interplay between exotic superfluidity and magnetism in a chain of four-component ultracold atoms, arXiv:1512.06669 submitted to Phys Rev Lett, 2015
M. Timár: Investigation of low energy optical properties of a $\pi$-conjugated polymer, OTDK Thesis, 2015
M. Timár: Investigation of low energy optical properties of a $\pi$-conjugated polymer, BME, 2015
G. Barcza: Nonlocal density matrix renormalization group applied to strongly correlated systems, ELTE, 2015
D. Jakab, E. Szirmai, M. Lewenstein, G. Szirmai: Competing valence bond and symmetry breaking Mott states of spin-3/2 fermions on a honeycomb lattice, http://arxiv.org/abs/1509.07362, submitted to Phys Rev B, 2015




 

Events of the project

  
2013-03-08 17:52:40
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