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Register a new userQuantum phase transition in the one-dimensional extended Peierls-Hubbard model
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We consider the one-dimensional extended Hubbard model in the presence of an explicit dimerization $delta$. For a sufficiently strong nearest neighbour repulsion we establish the existence of a quantum phase transition between a mixed bond-order wave and charge-density wave phase from a pure bond-order wave phase. This phase transition is in the universality class of the two-dimensional Ising model.
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For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with numerically exact data from the Density-Matrix Renormalization Group shows that the ground-state energy is quantitatively reliable for Coulomb parameters as large as the band width. The single-particle gap can almost triple from its bare Peierls value before substantial deviations appear. For the calculation of the dominant optical excitations, we follow two approaches. In Wannier theory, we perturb the Wannier exciton states to second order. In two-step perturbation theory, similar in spirit to the GW-BSE approach, we form excitons from dressed electron-hole excitations. We find the Wannier approach to be superior to the two-step perturbation theory. For singlet excitons, Wannier theory is applicable up to Coulomb parameters as large as half band width. For triplet excitons, second-order perturbation theory quickly fails completely.
Based on tensor network simulations, we discuss the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice described by the extended Fermi-Hubbard model. Considering different initial states, namely noninteracting, metallic, insulating spin and charge density waves, we identify several types of sudden interaction quenches which lead to dynamical criticality. In different scenarios, clear connections between DQPTs and particular properties of the mean double occupation or charge imbalance can be established. Dynamical transitions resulting solely from high-frequency time-periodic modulation are also found, which are well described by a Floquet effective Hamiltonian. State-of-the-art cold-atom quantum simulators constitute ideal platforms to implement several reported DQPTs experimentally.
We demonstrate that supervised machine learning (ML) with entanglement spectrum can give useful information for constructing phase diagram in the half-filled one-dimensional extended Hubbard model. Combining ML with infinite-size density-matrix renormalization group, we confirm that bond-order-wave phase remains stable in the thermodynamic limit.
Using time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest neighbor repulsion, U and V, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit non-monotonic dependence on V. For small and intermediate values of V, both velocities increase with V. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by V. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit, and an effective model in the strong-coupling regime.
We investigate the $T=0$ phase diagram of a variant of the one-dimensional extended Hubbard model where particles interact via a finite-range soft-shoulder potential. Using Density Matrix Renormalization Group (DMRG) simulations, we evidence the appearance of Cluster Luttinger Liquid (CLL) phases, similarly to what first predicted in a hard-core bosonic chain [M. Mattioli, M. Dalmonte, W. Lechner, and G. Pupillo, Phys. Rev. Lett. 111, 165302]. As the interaction strength parameters change, we find different types of clusters, that encode the order of the ground state in a semi-classical approximation and give rise to different types of CLLs. Interestingly, we find that the conventional Tomonaga Luttinger Liquid (TLL) is separated by a critical line with a central charge $c=5/2$, along which the two (spin and charge) bosonic degrees of freedom (corresponding to $c=1$ each) combine in a supersymmetric way with an emergent fermionic excitation ($c=1/2$). We also demonstrate that there are no significant spin correlations.
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