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arXiv:1904.09319 · Canadian Journal of Physics

Study of effective coupling between charge degrees of freedom in low dimensional hole-doped quantum antiferromagnets

Suraka Bhattacharjee, Ranjan Chaudhury

Published Sep 30, 2020• 0 citations
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Abstract

Expressions for the generalized charge stiffness constant at zero temperature are derived corresponding to low-dimensional hole-doped quantum antiferromagnets, describable by the t–J-like models, with a view to understanding fermionic pairing possibilities and charge couplings in itinerant antiferromagnetic systems. A detailed comparison between spin and charge correlations and couplings are presented for the strong and weak coupling limits in one (1D) and two (2D) dimensions. The result highlights that the charge and spin couplings show very similar behaviour in the over-doped region in both dimensions, whereas they show a completely different trend in the lower doping regimes. A qualitative equivalence of the generalized charge stiffness constant with the effective Drude weight and Coulomb interaction is established based on the comparison with other theoretical and experimental results. The fall in charge stiffness with increase in doping then implies a reduction in magnitude of the effective Coulomb repulsion between the mobile carriers. This leads to an enhanced possibility of fermionic pairing with an increase in doping concentration, in the possible presence of some other attraction-producing mechanism from a source outside the t–J-like models. Moreover, under certain conditions in the optimal doping region, the t–J-like models themselves are able to produce an attractive interaction for pairing.

DOI
10.1139/cjp-2020-0306

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Expressions for the generalized charge stiffness constant at zero temperature are derived corresponding to low-dimensional hole-doped quantum antiferromagnets, describable by the t–J-like models, with a view to understanding fermionic pairing possibilities and charge couplings in itinerant antiferromagnetic systems. A detailed comparison between spin and charge correlations and couplings are presented for the strong and weak coupling limits in one (1D) and two (2D) dimensions. The result highlights that the charge and spin couplings show very similar behaviour in the over-doped region in both dimensions, whereas they show a completely different trend in the lower doping regimes. A qualitative equivalence of the generalized charge stiffness constant with the effective Drude weight and Coulomb interaction is established based on the comparison with other theoretical and experimental results. The fall in charge stiffness with increase in doping then implies a reduction in magnitude of the effective Coulomb repulsion between the mobile carriers. This leads to an enhanced possibility of fermionic pairing with an increase in doping concentration, in the possible presence of some other attraction-producing mechanism from a source outside the t–J-like models. Moreover, under certain conditions in the optimal doping region, the t–J-like models themselves are able to produce an attractive interaction for pairing.
The magnetic correlation in one-dimensional doped quantum Heisenberg antiferromagnets is investigated on the basis of the single band t-J model at zero temperature in the strong correlation limit. An analytical expression for the generalized spin stiffness constant corresponding to this model is derived and then stiffness constant is numerically studied as a function of doping concentration. The presence of a maximum in the plot of this theoretically obtained total stiffness constant as a function of doping concentration, occurring at a finite doping, suggests the emergence of a tendency to form a new magnetic ordering of itinerant nature in the system in the low doping region and it's disappearance as the doping is increased further. This prediction of ours is quite novel and may be directly tested by independent experiments in future. Our results for spin stiffness constant are compared with those for the effective exchange constant extracted from the available experimental results obtained so far from the chains of YBa2_22​Cu3_33​O6+x_{6+x}6+x​ at low temperature and they show very similar behaviour as a function of doping concentration. This firmly establishes the role of spin stiffness constant as effective exchange constant for strongly correlated semi-itinerant systems in one-dimension. Our results in general receive good support from those based on other theoretical approaches.
The generalized spin stiffness constant for a doped quantum antiferromagnet has been investigated both analytically and numerically as a function of doping concentration at zero temperature, based on the strongly correlated t-J model on two-dimensional square lattice. The nature of the theoretical dependence of the stiffness constant on doping shows a striking similarity with that of the effective exchange constant, obtained from the combination of other theoretical and experimental techniques in the low doping region. This correspondence once again establishes that spin stiffness can very well play the role of an effective exchange constant even in the strongly correlated semi-itinerant systems. Our theoretical plot of the stiffness constant against doping concentration in the whole doping region exhibits the various characteristic features like a possible crossover in the higher doping regions and persistence of short range ordering even for very high doping with the complete vanishing of spin stiffness occurring only close to 100% doping. Our results receive very good support from various other theoretical approaches and also brings out a few limitations of some of them. Our detailed analysis highlights the crucial importance of the study of spin stiffness for the proper understanding of magnetic correlations in a semi-itinerant magnetic system described by the strongly correlated t-J model. Moreover, our basic formalism can also be utilized for determination of the effective exchange constant and magnetic correlations for itinerant magnetic systems, in general in a novel way.
The spin response functions for a doped strongly correlated quantum Heisenberg antiferromagnet, in the form of a t – J model, on low-dimensional lattices have been explored. In particular, the spin stiffness constant and the spin diffusion coefficient have been calculated as functions of doping concentration by different approaches for this model on a chain and on a square lattice. The occurrences of various possible magnetic phases, namely with long range and short range orders, and also a novel paramagnetic phase, have been predicted at zero temperature. Our conclusions regarding the phase diagram agree remarkably well with those from other recent theoretical approaches. Our results are discussed in the light of experimental results from the cuprates.
We study the phase diagram of the two-dimensional t-J-V model of holes in a two-dimensional antiferromagnet in the J\ensuremath{\gg}t limit. Here t is the hole hopping parameter, J is the exchange coupling between nearest-neighbor spins, and V is the nearest-neighbor electron-electron repulsion. We also include the possibility of Heisenberg-Ising anisotropy, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\ne}Jz{\mathit{J}}_{\mathit{z}}Jz​. We obtain a complete description for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\ll}Jz{\mathit{J}}_{\mathit{z}}Jz​ and approximate results for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=Jz{\mathit{J}}_{\mathit{z}}Jz​. There is no region of the zero-temperature phase diagram that supports a dilute gas of holes in an antiferromagnet. Rather, the system always phase separates into hole-rich and no-hole phases, a result we believe to be more general than the model we have considered. We find various hole-crystal phases and, at high hole density, we find a ``Fermi-liquid'' phase and at least two superfluid phases, one with a charge 2e and one with a charge 4e order parameter.
The interplay of spin and charge degrees of freedom is believed to underlie various unresolved phenomena in strongly correlated systems.Quantum simulators based on neutral atoms provide an excellent testbed for investigating such phenomena and resolving their microscopic origins.Up to now, the majority of experimental and theoretical studies has focused on systems with fermionic exchange statistics.Here we expand the existing cold atom toolbox through the use of negative temperature states, enabling us to realize an antiferromagnetic, bosonic t -J model in two spatial dimensions, subject to a strong staggered magnetic field in a quantum gas microscope.Through comparison of the spreading dynamics of a single hole in a Néel versus a spin-polarized initial state, we establish the relevance of memory effects resulting from the buildup of strong spin-charge correlations in the dynamics of charge carriers in antiferromagnets.We further numerically predict rich dynamics of pairs of doped holes, which we demonstrate to be bound by a similar memory effect, while their center-of-mass can expand freely.Our work paves the way for the systematic exploration of the effect of antiferromagnetic spin ordering on the properties of individual charge carriers as well as finite doping phases: Our study demonstrates that the staggered field can be used to single out the effect of antiferromagnetism and holds the prospect to prepare low-temperature states in the near future.
Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the t-J model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-T_{c} superconductivity.