Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau’s Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit ‘strange metal’ behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal—the ‘d-wave metal’. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian—the usual t–J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron ‘ring-exchange’ term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 19 April 2022
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Baym, G. & Pethick, C. Landau Fermi-Liquid Theory: Concepts and Applications (Wiley-VCH, Germany, 1991)
Schofield, A. J. Non-Fermi liquids. Contemp. Phys. 40, 95–115 (1999)
Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006)
Boebinger, G. S. An abnormal normal state. Science 323, 590–591 (2009)
Stewart, G. R. Non-Fermi-liquid behavior in d- and f-electron metals. Rev. Mod. Phys. 73, 797–855 (2001)
Gegenwart, P., Si, Q. & Steglich, F. Quantum criticality in heavy-fermion metals. Nature Phys. 4, 186–197 (2008)
Luttinger, J. M. Fermi surface and some simple equilibrium properties of a system of interacting fermions. Phys. Rev. 119, 1153–1163 (1960)
Anderson, P. W. & Zou, Z. “Normal” tunneling and “normal” transport: diagnostics for the resonating-valence-bond state. Phys. Rev. Lett. 60, 132–135 (1988)
Varma, C. M., Littlewood, P. B., Schmitt-Rink, S., Abrahams, E. & Ruckenstein, A. E. Phenomenology of the normal state of Cu-O high-temperature superconductors. Phys. Rev. Lett. 63, 1996–1999 (1989)
Senthil, T. Critical Fermi surfaces and non-Fermi liquid metals. Phys. Rev. B 78, 035103 (2008)
Faulkner, T., Iqbal, N., Liu, H., McGreevy, J. & Vegh, D. Strange metal transport realized by gauge/gravity duality. Science 329, 1043–1047 (2010)
Sachdev, S. Holographic metals and the fractionalized Fermi liquid. Phys. Rev. Lett. 105, 151602 (2010)
Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987)
Baskaran, G., Zou, Z. & Anderson, P. W. The resonating valence bond state and high-Tc superconductivity – a mean field theory. Solid State Commun. 63, 973–976 (1987)
Nagaosa, N. & Lee, P. A. Normal-state properties of the uniform resonating-valence-bond state. Phys. Rev. Lett. 64, 2450–2453 (1990)
Lee, P. A. & Nagaosa, N. Gauge theory of the normal state of high-T c superconductors. Phys. Rev. B 46, 5621–5639 (1992)
Wen, X.-G. & Lee, P. A. Theory of underdoped cuprates. Phys. Rev. Lett. 76, 503–506 (1996)
Anderson, P. W., Baskaran, G., Zou, Z. & Hsu, T. Resonating valence-bond theory of phase transitions and superconductivity in La2CuO4-based compounds. Phys. Rev. Lett. 58, 2790–2793 (1987)
Feigelman, M. V., Geshkenbein, V. B., Ioffe, L. B. & Larkin, A. I. Two-dimensional Bose liquid with strong gauge-field interaction. Phys. Rev. B 48, 16641–16661 (1993)
Cooper, R. A. et al. Anomalous criticality in the electrical resistivity of La2–x Sr x CuO4 . Science 323, 603–607 (2009)
Motrunich, O. I. & Fisher, M. P. A. d-wave correlated critical Bose liquids in two dimensions. Phys. Rev. B 75, 235116 (2007)
Sheng, D. N., Motrunich, O. I., Trebst, S., Gull, E. & Fisher, M. P. A. Strong-coupling phases of frustrated bosons on a two-leg ladder with ring exchange. Phys. Rev. B 78, 054520 (2008)
Block, M. S. et al. Exotic gapless Mott insulators of bosons on multileg ladders. Phys. Rev. Lett. 106, 046402 (2011)
Mishmash, R. V. et al. Bose metals and insulators on multileg ladders with ring exchange. Phys. Rev. B 84, 245127 (2011)
White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992)
White, S. R. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B 48, 10345–10356 (1993)
Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2003)
Shankar, R. Bosonization: how to make it work for you in condensed matter. Acta Phys. Polon. B 26, 1835–1867 (1995)
Lin, H.-H., Balents, L. & Fisher, M. P. A. Exact SO(8) symmetry in the weakly-interacting two-leg ladder. Phys. Rev. B 58, 1794–1825 (1998)
Fjærestad, J. O. & Marston, J. B. Staggered orbital currents in the half-filled two-leg ladder. Phys. Rev. B 65, 125106 (2002)
Balents, L. & Fisher, M. P. A. Weak-coupling phase diagram of the two-chain hubbard model. Phys. Rev. B 53, 12133–12141 (1996)
Ceperley, D., Chester, G. V. & Kalos, M. H. Monte Carlo simulation of a many-fermion study. Phys. Rev. B 16, 3081–3099 (1977)
Gros, C. Physics of projected wavefunctions. Ann. Phys. 189, 53–88 (1989)
Hellberg, C. S. & Mele, E. J. Phase diagram of the one-dimensional t-J model from variational theory. Phys. Rev. Lett. 67, 2080–2083 (1991)
Ceperley, D. M. Fermion nodes. J. Stat. Phys. 63, 1237–1267 (1991)
Halperin, B. I., Lee, P. A. & Read, N. Theory of the half-filled Landau level. Phys. Rev. B 47, 7312–7343 (1993)
Laughlin, R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983)
Normand, B. & Oleś, A. M. Circulating-current states and ring-exchange interactions in cuprates. Phys. Rev. B 70, 134407 (2004)
Sheng, D. N., Motrunich, O. I. & Fisher, M. P. A. Spin Bose-metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip. Phys. Rev. B 79, 205112 (2009)
Block, M. S., Sheng, D. N., Motrunich, O. I. & Fisher, M. P. A. Spin Bose-metal and valence bond solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder. Phys. Rev. Lett. 106, 157202 (2011)
Imada, M. & Miyake, T. Electronic structure calculation by first principles for strongly correlated electron systems. J. Phys. Soc. Jpn 79, 112001 (2010)
Troyer, M. & Wiese, U.-J. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94, 170201 (2005)
Polchinski, J. Low-energy dynamics of the spinon-gauge system. Nucl. Phys. B 422, 617–633 (1994)
Altshuler, B. L., Ioffe, L. B. & Millis, A. J. Low-energy properties of fermions with singular interactions. Phys. Rev. B 50, 14048–14064 (1994)
Calabrese, P. & Cardy, J. Entanglement entropy and quantum field theory. J. Stat. Mech. 2004, P06002 (2004)
Calabrese, P., Campostrini, M., Essler, F. & Nienhuis, B. Parity effects in the scaling of block entanglement in gapless spin chains. Phys. Rev. Lett. 104, 095701 (2010)
Hastings, M. B., González, I., Kallin, A. B. & Melko, R. G. Measuring Renyi entanglement entropy in quantum Monte Carlo simulations. Phys. Rev. Lett. 104, 157201 (2010)
Zhang, Y., Grover, T. & Vishwanath, A. Entanglement entropy of critical spin liquids. Phys. Rev. Lett. 107, 067202 (2011)
Corboz, P., Orús, R., Bauer, B. & Vidal, G. Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states. Phys. Rev. B 81, 165104 (2010)
Nandkishore, R., Metlitski, M. A. & Senthil, T. Orthogonal metals: the simplest non-Fermi liquids. Phys. Rev. B 86, 045128 (2012)
We thank T. Senthil, R. Kaul, L. Balents, S. Sachdev, A. Vishwanath and P. Lee for discussions. This work was supported by the NSF under the KITP grant PHY05-51164 and the MRSEC programme under award number DMR-1121053 (H.-C.J.), the NSF under grants DMR-1101912 (M.S.B., R.V.M., J.R.G. and M.P.A.F.), DMR-1056536 (M.S.B.), DMR-0906816 and DMR-1205734 (D.N.S.), DMR-0907145 (O.I.M.), and by the Caltech Institute of Quantum Information and Matter, an NSF Physics Frontiers Center with the support of the Gordon and Betty Moore Foundation (O.I.M. and M.P.A.F.). We also acknowledge support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC award (DMR-1121053), and an NSF grant (CNS-0960316).
The authors declare no competing financial interests.
About this article
Cite this article
Jiang, HC., Block, M., Mishmash, R. et al. Non-Fermi-liquid d-wave metal phase of strongly interacting electrons. Nature 493, 39–44 (2013). https://doi.org/10.1038/nature11732
This article is cited by
Nature Communications (2022)
Nature Physics (2022)
A novel strongly correlated electronic thin-film laser energy/power meter based on anisotropic Seebeck effect
Applied Physics A (2014)