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Tytuł:
Theoretical Approach to Strongly Correlated Systems Based on the U(1) and SU(2) Symmetry Groups
Autorzy:
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1431186.pdf
Data publikacji:
2012-04
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
74.20.-z
74.20.Fg
71.10.Pm
Opis:
The spin-rotationally invariant SU(2)×U(1) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated. We argue that in strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of 2π. Furthermore, it is shown that U(1) and SU(2) gauge fields play a similar role as phonons in the BCS theory: they act as the the "glue" for fermion pairing.
Źródło:
Acta Physica Polonica A; 2012, 121, 4; 738-743
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quantum Criticality Due to the Topological Effects in the Hubbard Model
Autorzy:
Kopeć, T. K.
Powiązania:
https://bibliotekanauki.pl/articles/2047311.pdf
Data publikacji:
2007-04
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
74.20.Fg
71.10.Pm
Opis:
We argue that in a strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of 2π. By unraveling consequences of the nontrivial topology of the charge gauge U(2) group, we found that the pinning of the chemical potential and the zero-temperature divergence of charge compressibility define a novel "hidden" quantum criticality on verge of the Mott transition governed by the protectorate of stable topological numbers rather than the Landau paradigm of the symmetry breaking.
Źródło:
Acta Physica Polonica A; 2007, 111, 4; 527-536
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological Criticality on Brink of the Mott Transition in High-T$\text{}_{c}$ Superconductors
Autorzy:
Kopeć, T. K.
Powiązania:
https://bibliotekanauki.pl/articles/2046733.pdf
Data publikacji:
2006-04
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
74.20.-z
74.20.Fg
71.10.Pm
Opis:
The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-T$\text{}_{c}$ cuprates. The theory includes the effects of the relevant energy scales with the emphasis on the Coulomb interaction $U$ governed by the electromagnetic U(1) compact group. The results are obtained for the layered t-t'-t$\text{}_{⊥}$-U-J system of strongly correlated electrons relevant for cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara "imaginary time", labelled by a topological winding numbers, governed by gauge flux changes by an integer multiple of 2π, are essential configurations of the phase field dual to the charge. The impact of these topological excitations is calculated for the phase diagram, which displays the "hidden" quantum critical point on verge of the Mott transition that is given by a divergence of the charge compressibility.
Źródło:
Acta Physica Polonica A; 2006, 109, 4-5; 499-506
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bose-Hubbard Model in the Rotating Frame of Reference
Autorzy:
Polak, T.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1536643.pdf
Data publikacji:
2010-08
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
05.30.Jp
03.75.Lm
03.75.Nt
Opis:
Following a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz we discuss the ground state of the two-dimensional Bose-Hubbard Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields. We derive an effective quantum action for the Bose-Hubbard model, which enables a non-perturbative treatment of the zero-temperature phase transition in the rotating frame. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f = 0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice. Performed calculations revealed strong non-monotonical dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.
Źródło:
Acta Physica Polonica A; 2010, 118, 2; 279-282
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pairing Scenarios for the Hubbard Model in the Strong Coupling Limit
Autorzy:
Apinyan, V.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1812294.pdf
Data publikacji:
2008-07
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
71.27.+a
71.10.Fd
74.20.Rp
Opis:
We consider a spin-rotationally invariant Hubbard model. The original electron operator is presented in the charge-spin-fermion U(1)×SU(2) factorized form. The factorization procedure is given in terms of the emergent gauge fields. As a result, the electron appears like a composite object consisting of strongly fluctuating phase field and spatially rotating spin axis. Furthermore, we elaborate microscopically on the form of possible pairing states.
Źródło:
Acta Physica Polonica A; 2008, 114, 1; 159-163
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Electron Spectral Functions in the Presence of the Antiferromagnetic Order in the Two-Dimensional Hubbard Model
Autorzy:
Zaleski, T.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1536615.pdf
Data publikacji:
2010-08
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
71.10.Fd
71.10.-w
71.10.Pm
Opis:
We use a recently proposed quantum SU(2)×U(1) rotor approach for the Hubbard model to calculate electronic spectral functions in a presence of an antiferromagnetic state for any value of the Coulomb interaction. We isolate the collective variables for charge and spin in the form of the space-time fluctuating U(1) phase field and SU(2) rotating spin quantization axis, respectively. As a result, the fermion Green function in the space-time domain becomes a product of a $CP^1$ propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. In turn, the spectral lines are obtained by performing the convolution of spin, charge and pseudo-fermion Green's functions. We observe an emergence of a sharp peak in the electron spectral functions within the antiferromagnetic phase, whose spectral weight is equal to the antiferromagnetic order parameter.
Źródło:
Acta Physica Polonica A; 2010, 118, 2; 267-272
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamic Structure Factor of Ultracold Bosons in Optical Lattice
Autorzy:
Zaleski, T.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1398602.pdf
Data publikacji:
2016-08
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
03.75.Hh
05.30.Jp
67.85.Hj
Opis:
Ultracold atoms in optical lattices have been intensively investigated in recent years as they provide a very well controllable environment for observation of many-body quantum phenomena, closely mimicking physics of strongly interacting electronic systems. Here, we use the quantum rotor approach supplemented by the Bogolyubov method to investigate one- and two-particle excitations, which are a measure of inter-particle correlations. We calculate one-particle spectral function and dynamic structure factor, which can be observed using spectroscopy of cold atomic systems. Our calculations require a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelised fast Fourier transform. We observe the appearance of sharp coherence peaks in the superfluid phase of the cold bosons, which closely resembles the formation of sharply defined quasiparticle excitations below $T_{c}$ in cuprates or smeared excitation spectra characteristic for strongly interacting systems.
Źródło:
Acta Physica Polonica A; 2016, 130, 2; 564-568
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ultra-Cold Bosons in Optical Lattice: Time-of-Flight Imaging of Atom-Atom Correlations
Autorzy:
Zaleski, T.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1431254.pdf
Data publikacji:
2012-04
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
03.75.Kk
05.30.Jp
67.85.Hj
Opis:
In the present paper, we investigate a system of strongly interacting bosons confined in two-dimensional optical lattice. We propose a combination of the Bogoliubov method with the quantum rotor approach and determine the spatial atom-atom correlations. This allows us to calculate time-of-flight absorption images, which exhibit all the characteristic features present in experimental results, namely transition from superfluid peaks to Mott insulating blob.
Źródło:
Acta Physica Polonica A; 2012, 121, 4; 796-800
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quantum Rotor Approach to the Mott-Insulator Transition in the Bose-Hubbard Model
Autorzy:
Polak, T.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1812265.pdf
Data publikacji:
2008-07
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
05.30.Jp
03.75.Lm
03.75.Nt
Opis:
We present the novel approach to the Bose-Hubbard model using the U(1) quantum rotor description. We formulate a problem in the phase only action using an effective action formalism and obtain analytical formulae for the critical lines. We show that the nontrivial U(1) phase field configurations have an impact on the phase diagrams. The topological character of the quantum field is governed by terms of the integer charges -- winding numbers n. The comparison of the presented results with recently obtained quantum Monte Carlo numerical calculations suggests that the competition between quantum effects in strongly interacting boson systems is correctly captured by our model.
Źródło:
Acta Physica Polonica A; 2008, 114, 1; 29-34
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Antiferromagnetic Order in the Hubbard Model: Spin-Charge Rotating Reference Frame Approach
Autorzy:
Zaleski, T.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1812334.pdf
Data publikacji:
2008-07
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
71.10.Fd
75.10.Jm
Opis:
We study the antiferromagnetic phase of three-dimensional Hubbard model with nearest neighbors hopping on a bipartite cubic lattice. We use the quantum SU(2)×U(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin-Wagner theorem. As our theory describes the evolution from a Slater (U ≪ t) to a Mott-Heisenberg (U ≫ t) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t.
Źródło:
Acta Physica Polonica A; 2008, 114, 1; 247-251
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Phase Transitions in Optical Lattices at Finite Temperatures
Autorzy:
Polak, T.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1810621.pdf
Data publikacji:
2009-01
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
05.30.Jp
03.75.Lm
03.75.Nt
67.40.Kh
Opis:
We discuss the finite-temperature phase diagram in three-dimensional Bose-Hubbard model relevant for the Bose-Einstein condensates in optical lattices, by employing U(1) quantum rotor approach and the topologically constrained path integral, that includes a summation over U(1) topological charge. The effective action formalism allows us to formulate a problem in the phase only action and obtain analytical formulae for the critical lines beyond mean-field theory.
Źródło:
Acta Physica Polonica A; 2009, 115, 1; 418-420
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Magnetically Driven Superconducting Pairing Interaction in the Two-Dimensional Hubbard Model within a Spin-Rotationally Invariant Approach
Autorzy:
Apinyan, V.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1536627.pdf
Data publikacji:
2010-08
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
71.10.Pm
74.20.Fg
74.72.-h
Opis:
The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. It is shown that these fields play a similar role as phonons in the BCS theory: they provide the "glue" for fermion pairing. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.
Źródło:
Acta Physica Polonica A; 2010, 118, 2; 273-278
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Two-Band Model for Coherent Excitonic Condensates
Autorzy:
Apinyan, V.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1398643.pdf
Data publikacji:
2016-08
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
71.10.Fd
71.28.+d
71.35.-y
71.10.Hf
Opis:
We consider the excitonic correlations in the two-band solid state system composed of the valence band and conduction band electrons. We treat the phase coherence mechanism in the system by presenting the electron operator as a fermion attached to the U(1) phase-flux tube. The emergent bosonic gauge field, related to the phase variables appears to be crucial for the coherent Bose-Einstein condensation of excitons. We calculate the normal excitonic Green functions, and the single-particle density of states functions being a convolution between bosonic and fermionic counterparts. We obtain the total density of states as a sum of two independent parts. For the coherent normal fermionic density of states, there is no hybridization-gap found in the system due to strong coherence effects and phase stiffness.
Źródło:
Acta Physica Polonica A; 2016, 130, 2; 621-624
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Phase Transitions of Bosons in Optical Lattices with a Mixture of Single and Pair Hoppings
Autorzy:
Travin, V.
Kopeć, T.
Powiązania:
https://bibliotekanauki.pl/articles/1398644.pdf
Data publikacji:
2016-08
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
67.10.Fj
67.85.Hj
67.90.+z
Opis:
We considered Bose condensate in optical lattice with mixture of single and pair hoppings for arbitrary temperatures. In order to calculate free energy of the system and determine phase transition lines between disordered and ordered phases, the Laplace transform method has been applied. We identified several possible scenarios for phase diagrams with phase transitions of the second kind. The results have been obtained from both analytical and numerical methods of calculation. Finally, we obtained thermal insensitivity of the system for big values of reduced pair hopping and (or) reduced chemical potential.
Źródło:
Acta Physica Polonica A; 2016, 130, 2; 625-628
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Superconducting Critical Temperature of Homologous Series of High-T$\text{}_{c}$ Cuprates as a Function of Number of Layers
Autorzy:
Zaleski, T. A.
Kopeć, T. K.
Powiązania:
https://bibliotekanauki.pl/articles/2038383.pdf
Data publikacji:
2004-11
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
74.20.-z
74.72.-h
74.50.+r
Opis:
We have considered a model of n-layer high-temperature cuprates of homologous series like HgBa$\text{}_{2}$Ca$\text{}_{n-1}$Cu$\text{}_{n}$O$\text{}_{2+2n+δ}$ to determine the dependence of the critical temperature T$\text{}_{c}$(n) on the number n of Cu-O planes in an elementary cell. Focusing on the description of the high-temperature superconducting system in terms of the collective phase variables, we have studied a semi-microscopic anisotropic three-dimensional vector XY model of stacked copper-oxide layers with adjustable parameters representing microscopic in-plane and out-of-plane phase stiffnesses. The model captures the layered composition and block structure along c-axis of superconducting homologous series. Implementing the spherical closure relation we have solved the phase XY model exactly with the help of transfer matrix method for vector variables. The calculated dependence of the critical temperature T$\text{}_{c}$(n) on the block size n is monotonic with n.
Źródło:
Acta Physica Polonica A; 2004, 106, 5; 561-567
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 60

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