Gauge Theory for a Doped Antiferromagnet in a Rotating Reference-Frame

Abstract

We study a doped antiferromagnet (AF) using a rotating reference-frame. Whereas in the laboratory reference-frame with a globally fixed spin-quantization axis (SQA) the long-wavelength, lowenergy physics is given by the O(3) non-linear σ-model with current-current interactions between the fermionic degrees of freedom and the order-parameter field for the spin-background, an alternative description in form of an U(1) gauge theory can be derived by choosing the SQA defined by the local direction of the order-parameter field via a SU(2) rotation of the fermionic spinor. Within a large-N expansion of this U(1) gauge theory we obtain the phase diagram for the doped AF and identify the relevant terms due to doping that lead to a quantum phase transition at T = 0 from the antiferromagnetically ordered Néel phase to the quantum-disordered (QD) spin-liquid phase. Furthermore, we calculate the propagator of the corresponding U(1) gauge field, which mediates a long-range transverse interaction between the bosonic and fermionic fields. It is found that the strength of the propagator is proportional to the gap of the spin-excitations. Therefore, we expect as a consequence of this long-range interaction the formation of bound states when the spin-gap opens, i.e. in the QD spin-liquid phase. The possible bound states are spin-waves with a (spin-) gap in the excitation spectrum, spinless fermions and pairs of fermions. Thus, an alternative picture for charge-spin separation emerges, with composite charge-separated excitations. Moreover, the present treatment shows an intimate connection between the opening of the spin-gap and charge-spin separation as well as pairing.

Unified picture of N el order destruction, d-wave superconductivity and the pseudogap phase for highTccuprates

“…Although the value of |λ ij | is probably very small compared to t, the important point is that it combines with the large parameter J K ∼ 1 eV [54,55], which leads to the Zhang-Rice singlet [60] in the limit of J K → ∞. The gauge field description is suitable for the non-perturbative effect arising from J K [41,61,62]. The characteristic energy scale is given by ω J λ = (J K /4) 2 + 4λ 2 (k F a) 2 , and for the high T c cuprates, ω J λ is large enough so that SC is scaled by F .…”

Basic aspects and main results of NMR-NQR spectroscopies in high-temperature superconductors

“…Doping and disorder (e.g. holes and/or spin vacancies) are expected to increase g (for the dependence of g on the hole content see Kubert and Muramatsu (1996)). For T > 0 (in practice one has to be at a temperature higher than the 3D ordering temperature T N in order to retain the 2D character of the system) La 2 CuO 4 should be in the renormalized classical (RC) regime, where ρ s and c sw are renormalized by quantum fluctuations with respect to their mean-field values.…”

Some remarks on pseudogap behavior of nearly antiferromagnetic metals

“…Will precursors of this effect show up and induce pseudo gaps in the paramagnetic phase for sufficiently large ξ? Pseudo gaps play an important role in the physics of underdoped cuprates [8][9][10][11][12][13][14][15] and it has been speculated that they are indeed precursors of gaps in either superconducting, antiferromagnetic, flux or striped phases. In this report we want to investigate qualitatively on the basis of simple physical arguments under what generic conditions such pseudo gaps are expected to occur close to an antiferromagnetic QCP.…”

“…To investigate the pseudo gap phase in this case, probably the most obvious theoretical route 24,7 to describe the adiabatic adjustment of the wave function of the electrons is to rotate the quantization axis of the electrons into the local direction of the slowly fluctuating order parameter. This approach has been used by a number of authors interested in the pseudo gap phase of the cuprates [9][10][11] . A natural model to discuss this type of physics consists of a non-linear σ-model coupled to the spin S(r) = 1 2 f † α (r)σ α,β f β (r) of fermions f .…”