Gutzwiller magnetic phase diagram of the undopedt−t′−UHubbard model

Abstract

We calculate the magnetic phase diagram of the half-filled t − t − U Hubbard model as a function of t and U , within the Gutzwiller approximation RPA (GA+RPA). As U increases, the system first crosses over to one of a wide variety of incommensurate phases, whose origin is clarified in terms of double nesting. We evaluate the stability regime of the incommensurate phases by allowing for symmetry-breaking with regard to the formation of spin spirals, and find a crossover to commensurate phases as U increases and a full gap opens. The results are compared with a variety of other recent calculations, and in general good agreement is found. For parameters appropriate to the cuprates, double occupancy should be only mildly suppressed in the absence of magnetic order, inconsistent with a strong coupling scenario.PACS numbers:

Gutzwiller charge phase diagram of cuprates, including electron–phonon coupling effects

“…In particular, the T = 0 magnetic phase diagram of the cuprates was derived using the time-dependent GA (TDGA) [22]. In the electron-doped cuprates, the magnetic phase diagram is dominated at all dopings by a commensurate π π ( , )antiferromagnetic (AFM) order [22]. In contrast, for the hole doped cuprates, we find a wide doping range over which the magnetic order is incommensurate.…”

“…Furthermore, at large doping cuprates behave as Fermi liquids, so that one can hope to obtain information on ordered phases by studying the instabilities that disrupt the Fermi liquid behavior, provided the correlated physics is included in the analysis. We have shown that in the weak and intermediate coupling range, peaks in the bare susceptibility of 2D materials, which determine magnetic instabilities, form a map of the FS, and the dominant instabilities are generally related to the double nesting features [15,22], where two branches of the map cross. In particular, the T = 0 magnetic phase diagram of the cuprates was derived using the time-dependent GA (TDGA) [22].…”

“…We have shown that in the weak and intermediate coupling range, peaks in the bare susceptibility of 2D materials, which determine magnetic instabilities, form a map of the FS, and the dominant instabilities are generally related to the double nesting features [15,22], where two branches of the map cross. In particular, the T = 0 magnetic phase diagram of the cuprates was derived using the time-dependent GA (TDGA) [22]. In the electron-doped cuprates, the magnetic phase diagram is dominated at all dopings by a commensurate π π ( , )antiferromagnetic (AFM) order [22].…”

“…We adopt an intermediate coupling approach in our analysis in this study [13]. This is justified by recent studies [14][15][16][17][18][19], which have indicated that correlations in the cuprates are not as strong as initially believed, and that cuprates fall, instead, in an intermediate coupling regime, with ⩽ ⩽ U t 6 9 , where U is the effective Hubbard interaction and t is the nearest-neighbor hopping parameter. We have shown [13] that intermediate coupling corresponds approximately to ⩽ ⩽ = U t U t 4 13.6 BR , where U BR is the mean-field Brinkman-Rice energy signaling the transition to the Mott insulating state [15,20].…”

“…We present the full evolution with doping of the leading charge-phonon instabilities for several families of cuprates, including La −x 2 A x CuO δ + 4 , A = Sr (LSCO) or Ba (LBCO) and Bi2201. The magnetic (charge) instabilities are usually determined by zeroes of the Stoner denominator, [22]…”