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arXiv:2011.10686 · Physical review. B./Physical review. B

Effect of phase string on single-hole dynamics in the two-leg Hubbard ladder

Kazuya Shinjo, Shigetoshi Sota, Takami Tohyama

Published Jan 25, 2021• 11 citations
arXivHTMLPDF

Abstract

Optical measurements in doped Mott insulators have discovered the emergence of spectral weights at mid-infrared (MIR) upon chemical doping and photodoping. MIR weights may have a relation to string-type excitation of spins, which is induced by a doped hole generating misarranged spins with respect to their sublattice. There are two types of string effects: one is an ${S}^{z}$ string that is reparable by quantum spin flips and the other is a phase string irreparable by the spin flips. We investigate the effect of ${S}^{z}$ and phase strings on MIR weights. Calculating the optical conductivity of the single-hole Hubbard model in the strong-coupling regime and the $t\text{\ensuremath{-}}J$ model on two-leg ladders by using time-dependent Lanczos and density-matrix renormalization group, we find that phase strings make a crucial effect on the emergence of MIR weights as compared with ${S}^{z}$ strings. Our findings indicate that a mutual Chern-Simons gauge field acting between spin and charge degrees of freedom, which is the origin of phase strings, is significant for obtaining MIR weights. Conversely, if we remove this gauge field, no phase is picked up by a doped hole. As a result, a spin polaron accompanied by a local spin distortion emerges and a quasiparticle with a cosinelike energy dispersion is formed in single-particle spectral function. Furthermore, we suggest a Floquet engineering to examine the phase-string effect in cold atoms.

DOI
10.1103/physrevb.103.035141

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Optical measurements in doped Mott insulators have discovered the emergence of spectral weights at mid-infrared (MIR) upon chemical doping and photodoping. MIR weights may have a relation to string-type excitation of spins, which is induced by a doped hole generating misarranged spins with respect to their sublattice. There are two types of string effects: one is an Sz{S}^{z}Sz string that is reparable by quantum spin flips and the other is a phase string irreparable by the spin flips. We investigate the effect of Sz{S}^{z}Sz and phase strings on MIR weights. Calculating the optical conductivity of the single-hole Hubbard model in the strong-coupling regime and the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model on two-leg ladders by using time-dependent Lanczos and density-matrix renormalization group, we find that phase strings make a crucial effect on the emergence of MIR weights as compared with Sz{S}^{z}Sz strings. Our findings indicate that a mutual Chern-Simons gauge field acting between spin and charge degrees of freedom, which is the origin of phase strings, is significant for obtaining MIR weights. Conversely, if we remove this gauge field, no phase is picked up by a doped hole. As a result, a spin polaron accompanied by a local spin distortion emerges and a quasiparticle with a cosinelike energy dispersion is formed in single-particle spectral function. Furthermore, we suggest a Floquet engineering to examine the phase-string effect in cold atoms.
We show that pronounced modulations in spin and charge densities can be induced by the insertion of a single hole in an otherwise half-filled two-leg Hubbard ladder. Accompanied with these modulations is a loosely bound structure of the doped charge with a spin-1/2, in contrast to the tightly bound case where such modulations are absent. These behaviors are caused by the interference of the Berry phases associated with a string of flipped spins (or ``phase strings'') left behind as a hole travels through a spin bath with a short-range antiferromagnetic order. The key role of the phase strings is also reflected in how the system responds to increasing spin polarization and the on-site repulsion, addition of a second hole, and increasing asymmetry between intra- and interchain hopping. Remarkably, all these properties persist down to ladders as short as $\ensuremath{\sim}10$ sites, as the smoking gun of the phase-string effect. They can therefore be studied in cold-atom experiments using the recently developed fermion microscope.
A long-standing issue in the physics of strongly correlated electronic systems is whether the motion of a single hole in quantum antiferromagnets can be understood in terms of the quasiparticle picture. Very recently, investigations of this issue have been within the experimental reach. Here we perform a large-scale density matrix renormalization group study, and provide the first unambiguous numerical evidence showing that in ladder systems, a single hole doped in the Mott antiferromagnet does not behave as a quasiparticle. Specifically, the injected hole is found to be always localized as long as the leg number is larger than one, with a vanishing quasiparticle weight and a localization length monotonically decreasing with the leg number. In addition, the single hole self-localization is insensitive to the parity (even-odd) of the leg number. Our findings may advance conceptual developments in different fields of condensed matter physics. First of all, the intriguing self-localization phenomenon is of pure strong correlation origin free of extrinsic disorders. Therefore, it is in sharp contrast to the well-known Anderson localization and recently found many-body localization, where extrinsic disordered potentials play crucial roles. Second, they confirm the analytical predictions of the so-called phase string theory, suggesting that the phase string effect lies in the core of the physics of doped Mott antiferromagnets.
We study the spectral function of two-leg Hubbard ladders with the time-dependent density matrix renormalization group method (tDMRG). The high-resolution spectrum displays features of spin-charge separation and a scattering continuum of excitations with coherent bands of bound states ``leaking'' from it. As the interleg hopping is increased, the continuum in the bonding channel moves to higher energies and spinon and holon branches merge into a single coherent quasiparticle band. Simultaneously, the spectrum undergoes a crossover from a regime with two minima at incommensurate values of kx{k}_{x}kx​ (a Mott insulator), to one with a single minimum at ${k}_{x}=\ensuremath{\pi}$ (a band insulator). We identify the presence of a continuum of scattering states consisting of a triplon and a polaron. We analyze the processes leading to quasiparticle formation by studying the time evolution of charge and spin degrees of freedom in real space after the hole is created. At short times, incoherent holons and spinons are emitted but after a characteristic time $\ensuremath{\tau}$ charge and spin form polarons that propagate coherently.
Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high Tc{T}_{c}Tc​ cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite $t\text{\ensuremath{-}}J$ ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.
In this paper, we have systematically studied the single-hole problem in two-leg Hubbard and $t\ensuremath{-}J$ ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.
The motion of a single hole in a Mott antiferromagnet is investigated based on the $t\ensuremath{-}J$ model. An exact expression of the energy spectrum is obtained, in which the irreparable phase string effect [Phys. Rev. Lett. 77, 5102 (1996)] is explicitly present. By identifying the phase string effect with spin backflow, we point out that spin-charge separation must exist in such a system: the doped hole has to decay into a neutral spinon and a spinless holon, together with the phase string. We show that while the spinon remains coherent, the holon motion is deterred by the phase string, resulting in its localization in space. We calculate the electron spectral function which explains the line shape of the spectral function as well as the ``quasiparticle'' spectrum observed in angle-resolved photoemission experiments. Other analytic and numerical approaches are discussed based on the present framework.