A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons

Abstract

The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott–Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron–phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.

Persistent current in a mesoscopic Holstein-Hubbard ring with Dresselhaus interaction

“…This happens because of the polaronic effect. As g 1 increases, the e-p interaction distorts the lattice more giving rise to a deeper polarization potential at the lattice sites which increases the effect of localization [28][29][30][31]. This causes a reduction in mobility of the electrons and as a result PCC decreases.…”

“…But, to our knowledge, very few studies have been reported in the presence of electron-phonon (e-p) interaction which can have important effects in mesoscopic systems. The effect of e-p interaction in such systems can be studied through the Holstein-Hubbard (HH) model [27][28][29][30][31][32]. Another important interaction which has drawn significant attention in the field of 'spintronics' is the spin-orbit interaction (SOI) [33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Metallicity in the Dissipative Hubbard-Holstein Model: Markovian and Non-Markovian Tensor-Network Methods for Open Quantum Many-Body Systems

“…E). We emphasize that in contrast to previous works, we made no strong assumptions about the phonons to render it more tractable [16,17].…”

“…Nevertheless, in the regime of intermediate electron-phonon interactions, the existence of a metallic phase has been established, in which light bipolarons can exist, yet with a much smaller pair-binding energy [14,15]. Recent theoretical studies considered the effect of anharmonicities on the properties of the metallic phase in the Hubbard-Holstein model, indicating the tendency to stabilize light bipolarons even at larger electron-phonon couplings [16,17], a crucial requirement for large transition tempera-Figure 1: Summary of our main finding: Dissipation tends to localize the bipolarons by means of effective, non-projective measurements. However, in the metallic regime, the bipolaronic binding energy remains mainly unaffected, i.e., bipolarons are stable even for strong dissipation.…”

Simultaneous fermion and exciton condensations from a model Hamiltonian

“…Model Hamiltonians are theoretical tools that are often useful in simulating the key physics associated with large-scale, highly-correlated systems. They are capable of modeling an array of quantum phases and many-body phenomena such as phase transitions [1][2][3][4][5], superconductivity [6][7][8][9][10], quantum magnetism [11][12][13][14], exciton condensation [15][16][17][18][19][20][21], lattice-like systems [22,23], etc. Additionally, model Hamiltonians which encompass nontrivial physics are often useful as benchmarks for theoretical tools such as many-body approximations [6,[24][25][26].…”