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Quantum Criticality Due to the Topological Effects in the Hubbard Model

100%
Kopeć T.
Acta Physica Polonica A
|
2007
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vol. 111
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issue 4
527-536
EN
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.
2
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Topological Criticality on Brink of the Mott Transition in High-T_c Superconductors

100%
Kopeć T.
Acta Physica Polonica A
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2006
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vol. 109
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issue 4-5
499-506
EN
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_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_⊥-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.
3
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Theoretical Approach to Strongly Correlated Systems Based on the U(1) and SU(2) Symmetry Groups

100%
Kopeć T.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
738-743
EN
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.
4
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Phase Transitions in Optical Lattices at Finite Temperatures

64%
Polak T., Kopeć T.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
418-420
EN
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.
5
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Phase Transitions of Bosons in Optical Lattices with a Mixture of Single and Pair Hoppings

64%
Travin V., Kopeć T.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
625-628
EN
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.
6
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Superconducting Critical Temperature of Homologous Series of High-T_c Cuprates as a Function of Number of Layers

64%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2004
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vol. 106
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issue 5
561-567
EN
We have considered a model of n-layer high-temperature cuprates of homologous series like HgBa_2Ca_{n-1}Cu_nO_{2+2n+δ} to determine the dependence of the critical temperature T_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_c(n) on the block size n is monotonic with n.
7
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The Existence of the 60 K Plateau in the YBa_2Cu_3O_{6+y} Phase Diagram: the Role of Oxygen Ordering and Charge Imbalance

64%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2007
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vol. 111
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issue 5
705-711
EN
We propose a semi-microscopic model of YBa_2Cu_3O_{6+y} to investigate the origin of the 60 K plateau in its phase diagram. Our model is a "phase only" approach to the high-temperature superconducting system in terms of collective variables. It is able to capture characteristic energy scales present in YBa_2Cu_3O_{6+y} by using adjustable parameters representing phase stiffnesses and allows for strong anisotropy within basal planes to simulate oxygen ordering. We solve the model calculated T_c for chosen system parameters investigating the influence of oxygen ordering and doping imbalance on the shape of YBa_2Cu_3O_{6+y} phase diagram. Our results suggest that the oxygen ordering alone does not seem to be responsible for the existence of the 60 K plateau. However, relying on experimental data unveiling that oxygen doping of YBa_2Cu_3O_{6+y} may introduce a significant charge imbalance between CuO_2 planes and other sites, we show that simultaneously the former are underdoped, while the latter - strongly overdoped almost in the whole region of oxygen doping in which YBa_2Cu_3O_{6+y} is superconducting. This provides two natural counter acting factors, which possibly lead to rise the 60 K plateau with increasing oxygen doping.
8
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Antiferromagnetic Order in the Hubbard Model: Spin-Charge Rotating Reference Frame Approach

64%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2008
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vol. 114
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issue 1
247-251
EN
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.
9
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Ultra-Cold Bosons in Optical Lattice: Time-of-Flight Imaging of Atom-Atom Correlations

64%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
796-800
EN
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.
10
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Two-Band Model for Coherent Excitonic Condensates

64%
Apinyan V., Kopeć T.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
621-624
EN
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.
11
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Dynamic Structure Factor of Ultracold Bosons in Optical Lattice

64%
Zaleski T., Kopeć T.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
564-568
EN
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.
12
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Bose-Hubbard Model in the Rotating Frame of Reference

64%
Polak T., Kopeć T.
|
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issue 2
279-282
EN
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.
13
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Quantum Rotor Approach to the Mott-Insulator Transition in the Bose-Hubbard Model

64%
Polak T., Kopeć T.
Acta Physica Polonica A
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2008
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vol. 114
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issue 1
29-34
EN
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.
14
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Magnetically Driven Superconducting Pairing Interaction in the Two-Dimensional Hubbard Model within a Spin-Rotationally Invariant Approach

64%
Apinyan V., Kopeć T.
|
|
issue 2
273-278
EN
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.
15
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Electron Spectral Functions in the Presence of the Antiferromagnetic Order in the Two-Dimensional Hubbard Model

64%
Zaleski T., Kopeć T.
|
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issue 2
267-272
EN
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.
16
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Pairing Scenarios for the Hubbard Model in the Strong Coupling Limit

64%
Apinyan V., Kopeć T.
Acta Physica Polonica A
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2008
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vol. 114
|
issue 1
159-163
EN
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.
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