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Advances in Ultrafast Condensed Phase Physics

Out-of-equilibrium Hubbard dimer within DPOA

Amir Eskandari-asl, Adolfo Avella

Published Apr 5, 2024• 0 citations
Publisher

Abstract

We have studied the Hubbard model on a dimer under the effect of an intense ultra-short laser pulse using the Dynamical Projective Operatorial Approach (DPOA). This shows how DPOA, stemming from the Composite Operator Method, can effectively tackle strongly correlated systems and real materials. To study the effect of the pump pulse on the anti-ferromagnetic-like order, we have analyzed the behavior of the double occupancy. It turns out that the pulse, in a specific range of its parameters, can drive the system in and out of the otherwise very robust anti-ferromagnetic-like phase that naturally emerges at half-filling and low temperatures. In such a situation, the system undergoes Rabi-like oscillations.

DOI
10.1117/12.3029502

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We have studied the Hubbard model on a dimer under the effect of an intense ultra-short laser pulse using the Dynamical Projective Operatorial Approach (DPOA). This shows how DPOA, stemming from the Composite Operator Method, can effectively tackle strongly correlated systems and real materials. To study the effect of the pump pulse on the anti-ferromagnetic-like order, we have analyzed the behavior of the double occupancy. It turns out that the pulse, in a specific range of its parameters, can drive the system in and out of the otherwise very robust anti-ferromagnetic-like phase that naturally emerges at half-filling and low temperatures. In such a situation, the system undergoes Rabi-like oscillations.
This thesis explores non-equilibrium phenomena in strongly correlated quantum systems, focusing on the half-filled one-dimensional Hubbard model at zero temperature in the thermodynamic limit. Using tensor network methods, particularly infinite matrix product states (iMPS), we simulate the real-time dynamics induced by optical pump pulses. A laser pulse is modeled by a time-dependent vector potential applied via the Peierls substitution, with dynamics computed using the infinite time-evolving block decimation (iTEBD) algorithm. We investigate the emergence of a superconducting-like eta-pairing state with off-diagonal long-range order (ODLRO) and confirm that eta-pairing correlations are significantly enhanced for certain pulse parameters. Additionally, signatures of dynamical quantum phase transitions (DQPTs) are observed in the Loschmidt echo rate function. Finite-entanglement scaling is employed to extract the central charge and analyze criticality of the ground state.
The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any non-zero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases.
PACS. 71.10.−w – Theories and models of many electron systems. PACS. 71.10.Fd – Lattice fermion models. PACS. 71.15.Th – Other methods. Abstract. – The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases. Introduction. – New materials whose physics is dominated by electron correlations in narrow energy bands are actually a challenge for solid state physicists. The treatment of such systems is not trivial due to the competition between itinerant and localized behaviour of the electrons in these bands. The Hubbard Hamiltonian [1] is regarded as the simplest model
The electronic states of the two-dimensional Hubbard model are investigated by means of a 4-pole approximation within the composite operator method. In addition to the conventional Hubbard operators, we consider other two operators which come from the hierarchy of the equations of motion and carry information regarding nearest-neighbor spin and charge configurations. By means of this operatorial basis, we can study the physics related to the energy scale of J=4t2∕UJ=4{t}^{2}∕UJ=4t2∕U in addition to the one of UUU. Present results show relevant physical features, well beyond those previously obtained by means of a 2-pole approximation, such as a four-band structure with shadow bands and a quasiparticle peak at the Fermi level. The Fermi level stays pinned to the band flatness located at $(\ensuremath{\pi},0)$-point within a wide range of hole-doping $(0\ensuremath{\leqslant}\ensuremath{\delta}\ensuremath{\leqslant}0.15)$. A comprehensive analysis of double occupancy, internal energy, specific heat and entropy features have also been performed. All reported results are in excellent agreement with the data of numerical simulations.
We investigate the ultrafast optical response of the one-dimensional half-filled extended Hubbard model exposed to two successive laser pulses. By using the time-dependent Lanczos method, we find that following the first pulse, the excitation and deexcitation process between the ground state and excitonic states can be precisely controlled by the relative temporal displacement of the pulses. The underlying physics can be understood in terms of a modified Rabi model. Our simulations clearly demonstrate the controllability of ultrafast transition between excited and deexcited phases in strongly correlated electron systems.
Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal–insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, Z 2 slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of the Z 2 slave-spin method by studying a two-site Hubbard model. After exploring aspects of properties of this toy model, we make a comparative analysis of the results obtained by three methods: (i) slave-spin method on mean-field level, (ii) slave-spin method with gauge constraint, and (iii) the exact solution as a benchmark. We find that, protected by the particle–hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both U and T are small enough, the slave-spin mean-field method is also reliable in calculating the dynamic and thermal dynamic properties. However, when U or T is considerably large, the mean-field approximation gives ill-defined behaviors, which result from the unphysical states in the enlarged Hilbert space. These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints. Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.