Chen, Büttner, and Voit Reply

Abstract

Chen, Bü ttner, and Voit Reply In the preceding Comment [1], Capriotti et al. argue that the next-nearestneighbor spin-Peierls operatorÔ O nnn P l ÿ1 l S l S l2 is an irrelevant perturbation for the Heisenberg chain in the regime of weak frustration and hence the claim of our Letter [2] of the existence of an intermediate fixed point is unreasonable. In Ref. [2], we investigated the physical effect of the operatorÔ O nnn by renormalization group (RG) analysis. Recently, a related work was carried out by Sarkar and Sen [3] and the same bosonized operator of O O nnn is obtained. However, the main discrepancy between our work and Refs. [1,3] is that we kept the bosonized operator ofÔ O nnn and analyzed it by RG, while they just discarded it by giving an argument of the irrelevance of O O nnn . For an anisotropic XXZ chain, our RG result indeed indicates that the operatorÔ O nnn is irrelevant [2] in the meaning that it does not drive the system to a new phase, and this is consistent with that of Refs. [1,3]. But the main difference lies in the issue of whether an intermediate fixed point exists and whether this fixed point corresponds to a phase different from a Luttinger liquid.Despite the discussions in Ref.[1], we think that the scheme of discarding the operatorÔ O nnn based on its irrelevance seems to be oversimplified. We notice first that the magnetization curve of the Heisenberg model with an additional operatorÔ O nnn [4] gives an obvious different magnetization susceptibility from the one with-outÔ O nnn , which is a signal of the renormalization of the spin velocity. A complete scheme to deal withÔ O nnn should give a correct description of the induced effect not only on the weak frustration region but also on the strong frustration region. Furthermore, the omission ofÔ O nnn could not give any explanation why the operatorÔ O nnn shrinks the spin gap sizes in the regime of strong frustration [2,5]. In contrast to Ref.[1], our RG analysis gives a qualitative explanation of the influence ofÔ O nnn on spin gap sizes, which is consistent with the known result of the difference in gap sizes between the Majumdar-Ghosh and sawtooth chains [5,6].Based on the RG analysis we gave an argument for a vanishing spin-wave velocity and thus explained the in-

Pair Density Wave in the Pseudogap State of High Temperature Superconductors

“…In Refs. [21,26], it was argued that the energy dependence of the tunneling intensity can be used to identify the type of ordering in the superconducting state.In this Letter, we focus on the STM resolved modulations of the DOS in the pseudogap state and propose that these are a consequence of a novel density wave associated with d-wave Cooper pairs, first proposed in the context of the charge ordering in the vicinity of vortices [20,24]. This state, illustrated in Fig.…”

“…In this Letter, we focus on the STM resolved modulations of the DOS in the pseudogap state and propose that these are a consequence of a novel density wave associated with d-wave Cooper pairs, first proposed in the context of the charge ordering in the vicinity of vortices [20,24]. This state, illustrated in Fig.…”

“…The pseudogap modulations bears similarity to those observed near the vortex cores [20], but seems to be distinct from the STM features in the superconducting state [1,21,22], which exhibit energy dispersion. The origin of DOS modulation in the superconducting state has been for the most part attributed to quantum interference of quasi-particles [23], although potential relevance of electronic ordering has also been considered [21,24,25,26,27,28]. In Refs.…”

“…(1) of Ref. [24], has a rotationally symmetric charge periodicity of 4a × 4a near doping level x = 1/8. This state also arises naturally in the plaquette boson approach of Altman and Auerbach [29] or in the large N approximation of the t − J model [28].…”

Vortex core excitations in superconductors with frustrated antiferromagnetism

“…The discrepancy between the earlier theoretical prediction and the experimental observation stimulated various explanations. Recent intensive experimental [23,24,25,26,27] and theoretical [28,29,30,31,32,33] studies seem to converge on an explanation in terms of the field-induced AF around the vortex core. When the AF is frustrated on a triangular lattice [34,35], one would expect a different nature of electronic excitations near the vortex.…”