Quantum entanglement and the phases of matter

qpt.physics.harvard.edu

Quantum entanglement and the phases of matter

Quantum entanglementand the phases of matterTIFR, MumbaiJanuary 17, 2012Tuesday, January 17, 2012sachdev.physics.harvard.eduHARVARD


Quantum Entanglement: quantum superpositionwith more than one particleTuesday, January 17, 2012


Quantum Entanglement: quantum superpositionHydrogen atom:with more than one particleHydrogen molecule:= _= 1 √2(|↑↓ − |↓↑)Superposition of two electron states leads to non-localcorrelations between spinsTuesday, January 17, 2012


Quantum Entanglement: quantum superpositionwith more than one particle_Tuesday, January 17, 2012


Quantum Entanglement: quantum superpositionwith more than one particle_Tuesday, January 17, 2012


Quantum Entanglement: quantum superpositionwith more than one particle_Tuesday, January 17, 2012


Quantum Entanglement: quantum superpositionwith more than one particle_Einstein-Podolsky-Rosen “paradox”: Non-localcorrelations between observations arbitrarily far apartTuesday, January 17, 2012


Outline1. Quantum critical points and string theoryEntanglement and emergent dimensions2. High temperature superconductorsand strange metalsHolography of compressible quantum phasesTuesday, January 17, 2012


Outline1. Quantum critical points and string theoryEntanglement and emergent dimensions2. High temperature superconductorsand strange metalsHolography of compressible quantum phasesTuesday, January 17, 2012


Square lattice antiferromagnetH = ijJ ij Si · S jS=1/2spinsJJ/λExamine ground state as a function of λTuesday, January 17, 2012


Square lattice antiferromagnetH = ijJ ij Si · S jJJ/λ= √ 1 ↑↓ − ↓↑2λAt large ground state is a “quantum paramagnet” withspins locked in valence bond singletsTuesday, January 17, 2012


Square lattice antiferromagnetH = ijJ ij Si · S jJJ/λ= √ 1 ↑↓ − ↓↑2Nearest-neighor spins are “entangled” with each other.Can be separated into an Einstein-Podolsky-Rosen (EPR) pair.Tuesday, January 17, 2012


Square lattice antiferromagnetH = ijJ ij Si · S jJJ/λFor λ ≈ 1, the ground state has antiferromagnetic (“Néel”) order,and the spins align in a checkerboard patternTuesday, January 17, 2012


Square lattice antiferromagnetH = ijJ ij Si · S jJJ/λFor λ ≈ 1, the ground state has antiferromagnetic (“Néel”) order,and the spins align in a checkerboard patternNo EPR pairsTuesday, January 17, 2012


= 1 √ ↑↓ 2λ c− ↓↑λTuesday, January 17, 2012


= 1 √ ↑↓ 2λ c− ↓↑λPressure in TlCuCl3A. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka,Journal of the Physical Society of Japan, 73, 1446 (2004).Tuesday, January 17, 2012


TlCuCl 3An insulator whose spin susceptibility vanishesexponentially as the temperature T tends to zero.Tuesday, January 17, 2012


TlCuCl 3Quantum paramagnet atambient pressureTuesday, January 17, 2012


TlCuCl 3Neel order under pressureA. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka,Journal of the Physical Society of Japan, 73, 1446 (2004).Tuesday, January 17, 2012


= 1 √ ↑↓ 2λ c− ↓↑λTuesday, January 17, 2012


Excitation spectrum in the paramagnetic phaseλ cSpin S =1λ“triplon”Tuesday, January 17, 2012


Excitation spectrum in the paramagnetic phaseλ cSpin S =1λ“triplon”Tuesday, January 17, 2012


Excitation spectrum in the paramagnetic phaseλ cSpin S =1λ“triplon”Tuesday, January 17, 2012


Excitation spectrum in the paramagnetic phaseλ cSpin S =1λ“triplon”Tuesday, January 17, 2012


Excitation spectrum in the paramagnetic phaseλ cSpin S =1“triplon”λTuesday, January 17, 2012


Excitation spectrum in the Néel phaseλ cλSpin wavesTuesday, January 17, 2012


Excitation spectrum in the Néel phaseλ cλSpin wavesTuesday, January 17, 2012


Excitation spectrum in the Néel phaseλ cλSpin wavesTuesday, January 17, 2012


Excitations of TlCuCl 3 with varying pressure1.21Energy [meV]0.80.60.40.200 0.5 1 1.5 2 2.5 3Pressure [kbar]Tuesday, January 17, 2012Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer,Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)


Excitations of TlCuCl 3 with varying pressure1.21Energy [meV]0.80.60.40.2Broken valence bondexcitations of thequantum paramagnet00 0.5 1 1.5 2 2.5 3Pressure [kbar]Tuesday, January 17, 2012Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer,Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)


Excitations of TlCuCl 3 with varying pressure1.21Energy [meV]0.80.60.4Spin waves abovethe Néel state0.200 0.5 1 1.5 2 2.5 3Pressure [kbar]Tuesday, January 17, 2012Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer,Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)


Excitations of TlCuCl 3 with varying pressure1.21Energy [meV]0.80.60.4Longitudinal excitations–similar to the Higgs bosonFirst observation of the Higgs !0.200 0.5 1 1.5 2 2.5 3Pressure [kbar]Tuesday, January 17, 2012Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer,Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)


Excitations of TlCuCl 3 with varying pressure1.21Energy [meV]0.80.60.4Longitudinal excitations–similar to the Higgs bosonFirst observation of the Higgs !0.200 0.5 1 1.5 2 2.5 3Pressure [kbar]“Higgs” particle appears at theoretically predicted energyS. Sachdev, arXiv:0901.4103Tuesday, January 17, 2012Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer,Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)


= 1 √ ↑↓ 2λ c− ↓↑λTuesday, January 17, 2012


= √ 1 ↑↓ − ↓↑2λ cλQuantum critical point with non-localentanglement in spin wavefunctionTuesday, January 17, 2012


Tensor network representation of entanglementat quantum critical pointD-dimensionalspacedepth ofentanglementTuesday, January 17, 2012


Characteristics ofquantum critical point• Long-range entanglement• Long distance and low energy correlations near thequantum critical point are described by a quantumfield theory which is relativistically invariant (wherethe spin-wave velocity plays the role of the velocityof “light”).• The quantum field theory is invariant under scale andconformal transformations at the quantum criticalpoint: a CFT3Tuesday, January 17, 2012


Characteristics ofquantum critical point• Long-range entanglement• Long distance and low energy correlations near thequantum critical point are described by a quantumfield theory which is relativistically invariant (wherethe spin-wave velocity plays the role of the velocityof “light”).• The quantum field theory is invariant under scale andconformal transformations at the quantum criticalpoint: a CFT3Tuesday, January 17, 2012


Characteristics ofquantum critical point• Long-range entanglement• Long distance and low energy correlations near thequantum critical point are described by a quantumfield theory which is relativistically invariant (wherethe spin-wave velocity plays the role of the velocityof “light”).• The quantum field theory is invariant under scale andconformal transformations at the quantum criticalpoint: a CFT3Tuesday, January 17, 2012


String theory• Allows unification of the standard model of particlephysics with gravity.• Low-lying string modes correspond to gauge fields,gravitons, quarks . . .Tuesday, January 17, 2012


• A D-brane is a D-dimensional surface on which strings can end.• The low-energy theory on a D-brane is an ordinary quantumfield theory with no gravity.• In D = 2, we obtain strongly-interacting CFT3s. These are“dual” to string theory on anti-de Sitter space: AdS4.Tuesday, January 17, 2012


CFT D+1• A D-brane is a D-dimensional surface on which strings can end.• The low-energy theory on a D-brane is an ordinary quantumfield theory with no gravity.• In D = 2, we obtain strongly-interacting CFT3s. These are“dual” to string theory on anti-de Sitter space: AdS4.Tuesday, January 17, 2012


Tensor network representation of entanglementat quantum critical pointD-dimensionalspacedepth ofentanglementTuesday, January 17, 2012M. Levin and C. P. Nave, Phys. Rev. Lett. 99, 120601 (2007)F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)


String theory neara D-braneD-dimensionalspaceEmergent depth of directionentanglement of AdS4Tuesday, January 17, 2012


Tensor network representation of entanglementat quantum critical pointD-dimensionalspaceEmergent depth of directionentanglement of AdS4Tuesday, January 17, 2012Brian Swingle, arXiv:0905.1317


Entanglement entropyBAρ A =Tr B ρ = density matrix of region AEntanglement entropy S EE = −Tr (ρ A ln ρ A )Tuesday, January 17, 2012


Entanglement entropyAD-dimensionalspacedepth ofentanglementTuesday, January 17, 2012


Entanglement entropyAD-dimensionalspaceDraw a surface which intersects the minimal number of linksEmergent depth of directionentanglement of AdS4Tuesday, January 17, 2012


Entanglement entropyThe entanglement entropy of a region A on the boundaryequals the minimal area of a surface in the higher-dimensionalspace whose boundary co-incides with that of A.This can be seen both the string and tensor-network picturesS. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 18160 (2006).Brian Swingle, arXiv:0905.1317Tuesday, January 17, 2012


AdS d+2 R d,1MinkowskiCFT d+1Quantummatter withlong-rangeentanglementrEmergent holographic directionJ. McGreevy, arXiv0909.0518Tuesday, January 17, 2012


AdS d+2 R d,1MinkowskiCFT d+1AQuantummatter withlong-rangeentanglementrEmergent holographic directionTuesday, January 17, 2012


AdS d+2 R d,1MinkowskiCFT d+1AreameasuresentanglemententropyrAEmergent holographic directionQuantummatter withlong-rangeentanglementTuesday, January 17, 2012


= √ 1 ↑↓ − ↓↑2λ cλQuantum critical point with non-localentanglement in spin wavefunctionTuesday, January 17, 2012


S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).QuantumcriticalClassicalspinwavesDilutetriplongasNeel orderPressure in TlCuCl3Tuesday, January 17, 2012


S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).QuantumcriticalClassicalspinwavesDilutetriplongasNeel orderPressure in TlCuCl3Tuesday, January 17, 2012


S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).QuantumcriticalClassicalspinwavesDilutetriplongasShort-rangeentanglementShort-rangeentanglementNeel orderPressure in TlCuCl3Tuesday, January 17, 2012


S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).QuantumcriticalClassicalspinwavesDilutetriplongasNeel orderPressure in TlCuCl3Tuesday, January 17, 2012


S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).Excitations of a ground statewith long-range entanglementQuantumcriticalClassicalspinwavesDilutetriplongasNeel orderPressure in TlCuCl3Tuesday, January 17, 2012


AdS/CFT correspondence at non-zero temperaturesAdS4-Schwarzschild black-braneA 2+1dimensionalsystem at itsquantumcritical pointTuesday, January 17, 2012


AdS/CFT correspondence at non-zero temperaturesAdS4-Schwarzschild black-braneBlack-brane attemperature of2+1 dimensionalquantum criticalsystemA 2+1dimensionalsystem at itsquantumcritical pointTuesday, January 17, 2012


AdS/CFT correspondence at non-zero temperaturesAdS4-Schwarzschild black-braneA 2+1dimensionalsystem at itsquantumcritical pointBlack-brane attemperature of2+1 dimensionalquantum criticalsystemFriction of quantumcriticality = wavesfalling into black braneTuesday, January 17, 2012


AdS/CFT correspondence at non-zero temperaturesAdS4-Schwarzschild black-braneA 2+1dimensionalsystem at itsquantumcritical pointBlack-brane attemperature of2+1 dimensionalquantum criticalsystemProvides successful descriptionof many properties of quantumcritical points at non-zerotemperaturesTuesday, January 17, 2012


Outline1. Quantum critical points and string theoryEntanglement and emergent dimensions2. High temperature superconductorsand strange metalsHolography of compressible quantum phasesTuesday, January 17, 2012


Outline1. Quantum critical points and string theoryEntanglement and emergent dimensions2. High temperature superconductorsand strange metalsHolography of compressible quantum phasesTuesday, January 17, 2012


The cuprate superconductorsDavisTuesday, January 17, 2012


Square lattice antiferromagnetH = ijJ ij Si · S jGround state has long-range Néel orderTuesday, January 17, 2012


HoledopedElectrondopedTuesday, January 17, 2012


HoledopedElectrondopedSuperconductorBose condensate of pairs of electronsShort-range entanglementTuesday, January 17, 2012


Electron-doped cuprate superconductorsHoledopedElectrondopedTuesday, January 17, 2012


Electron-doped cuprate superconductorsHoledopedElectrondopedn 21.5 AF1Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, andR. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).Resistivity∼ ρ 0 + AT nTuesday, January 17, 2012


Electron-doped cuprate superconductorsHoledopedElectrondopedn 21.5 AF1Ordinary metalFigure prepared(Fermi by K. Jinliquid)and and R. L. Greenebased on N. P. Fournier, P. Armitage, andR. L. Short-range Greene, Rev. Mod. entanglementPhys. 82, 2421 (2010).Resistivity∼ ρ 0 + AT nTuesday, January 17, 2012


Electron-doped cuprate superconductorsHoledopedElectrondopedn 21.5 AF1Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, andR. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).Resistivity∼ ρ 0 + AT nTuesday, January 17, 2012


Electron-doped cuprate superconductorsStrangeMetalHoledopedElectrondopedn 21.5 AF1Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, andR. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).Resistivity∼ ρ 0 + AT nTuesday, January 17, 2012


Electron-doped cuprate superconductorsStrangeMetalHoledopedElectrondopedn 21.5 AF1Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, andR. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).Resistivity∼ ρ 0 + AT nTuesday, January 17, 2012


Electron-doped cuprate superconductorsStrangeMetalExcitations of a ground statewith long-range entanglement HoledopedElectrondopedn 21.5 AF1Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, andR. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).Resistivity∼ ρ 0 + AT nTuesday, January 17, 2012


Iron pnictides:a new class of high temperature superconductors150100OrtTetIshida, Nakai, and HosonoarXiv:0906.2045v150AFM/ Ort0SC0 0.02 0.04 0.06 0.08 0.10 0.12S. Nandi, M. G. Kim, A. Kreyssig, R. M. Fernandes, D. K. Pratt, A. Thaler, N. Ni,S. L. Bud'ko, P. C. Canfield, J. Schmalian, R. J. McQueeney, A. I. Goldman,Physical Review Letters 104, 057006 (2010).Tuesday, January 17, 2012


Temperature-doping phase diagram of theiron pnictides:BaFe 2 (As 1-x P x ) 2T 0T SDWT cSDWAF! "2.01.0Resistivity∼ ρ 0 + AT αSuperconductivity0Tuesday, January 17, 2012S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,Physical Review B 81, 184519 (2010)


Temperature-doping phase diagram of theiron pnictides:BaFe 2 (As 1-x P x ) 2T 0T SDWT cSDWAF! "2.01.0Resistivity∼ ρ 0 + AT αSuperconductivity0Tuesday, January 17, 2012Ordinary metal(Fermi liquid)S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,Short-range entanglementPhysical Review B 81, 184519 (2010)


Temperature-doping phase diagram of theiron pnictides:BaFe 2 (As 1-x P x ) 2T 0T SDWT cSDWAF! "2.01.0Resistivity∼ ρ 0 + AT αSuperconductivity0Tuesday, January 17, 2012S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,Physical Review B 81, 184519 (2010)


Temperature-doping phase diagram of theiron pnictides:StrangeMetalBaFe 2 (As 1-x P x ) 2T 0T SDWT c! "SDWAF2.01.0Resistivity∼ ρ 0 + AT αSuperconductivity0Tuesday, January 17, 2012S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,Physical Review B 81, 184519 (2010)


Temperature-doping phase diagram of theiron pnictides:StrangeMetalBaFe 2 (As 1-x P x ) 2T 0T SDWT c! "SDWAF2.01.0Resistivity∼ ρ 0 + AT αSuperconductivity0Tuesday, January 17, 2012S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,Physical Review B 81, 184519 (2010)


Temperature-doping phase diagram of theiron pnictides:Excitations of a ground statewith long-range entanglementStrangeMetalBaFe 2 (As 1-x P x ) 2T 0T SDWT c! "SDWAF2.01.0Resistivity∼ ρ 0 + AT αSuperconductivity0Tuesday, January 17, 2012S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,Physical Review B 81, 184519 (2010)


Temperature-pressure phase diagram ofan organic superconductorAFN. Doiron-Leyraud, P. Auban-Senzier, S. Rene de Cotret, A. Sedeki, C. Bourbonnais, D. Jerome,K. Bechgaard, and Louis Taillefer, Physical Review B 80, 214531 (2009)Tuesday, January 17, 2012


ermion sysndirectRuctionwhichs mediateddo interacramagneticmoment ofth interacofthe 4fpressure ishe position. ThereforeG. Knebel, D. Aoki, and J. Flouquet, arXiv:0911.5223.Tuson Park, F. FIG. Ronning, 2. H. Pressure–temperature Q. Yuan, M. B. Salamon, R. phase Movshovich, diagram of CeRhIJ. L. Sarrao, and zero J. D. Thompson, magnetic Nature field determined 440, 65 (2006) from specific heat meay the critisameorderase transiothe para-Tuesday, January 17, 2012Temperature-pressure phase diagram ofan heavy-fermion superconductor


Ordinary metals (Fermi liquids)Metal with “large”Fermi surfaceMomenta withelectron statesoccupiedMomenta withelectron statesemptyTuesday, January 17, 2012


Fermi surface+antiferromagnetismMetal with “large”Fermi surface+The electron spin polarization obeysS(r, τ)= ϕ (r, τ)e iK·rwhere K is the ordering wavevector.Tuesday, January 17, 2012


Fermi surface+antiferromagnetismIncreasing SDW orderAFϕ =0ϕ =0Metal with electronand hole pocketsMetal with “large”Fermi surfaceIncreasing interactionFermi surface reconstruction andonset of antiferromagnetismTuesday, January 17, 2012


Fermi surface+antiferromagnetismIncreasing SDW orderAFϕ =0ϕ =0Metal with electronand hole pocketsMetal with “large”Fermi surfaceIncreasing interactionFermi surface reconstruction andonset of antiferromagnetismTuesday, January 17, 2012


Fermi surface+antiferromagnetismIncreasing SDW orderAFϕ =0Quantum criticalpoint realizes astrongly-coupled“strange metal”with long-rangeϕ =0 entanglement !Metal with electronand hole pocketsMetal with “large”Fermi surfaceIncreasing interactionFermi surface reconstruction andonset of antiferromagnetismTuesday, January 17, 2012


TAF metalwith “small”Fermi pocketsIncreasing SDW orderFermi liquidwith “large”Fermi surfacesTuesday, January 17, 2012


D.J. Scalapino, E. Loh, and J.E. Hirsch, Phys. Rev. B 34, 8190 (1986)Ar. Abanov, A. V. Chubukov, and A. M. Finkel'stein, Europhys. Lett. 54, 488 (2001)S. Raghu, S.A. Kivelson, and D.J. Scalapino, Phys. Rev. B 81, 224505 (2010)M. A. Metlitski and S. Sachdev, Phys. Rev. B 85, 075127 (2010)TAF metalwith “small”Fermi pocketsIncreasing SDW orderHigh temperatureSuperconductor Fermi liquidwith “large”Fermi surfacesDavisTuesday, January 17, 2012


D.J. Scalapino, E. Loh, and J.E. Hirsch, Phys. Rev. B 34, 8190 (1986)Ar. Abanov, A. V. Chubukov, and A. M. Finkel'stein, Europhys. Lett. 54, 488 (2001)S. Raghu, S.A. Kivelson, and D.J. Scalapino, Phys. Rev. B 81, 224505 (2010)M. A. Metlitski and S. Sachdev, Phys. Rev. B 85, 075127 (2010)TAF metalwith “small”Fermi pocketsIncreasing SDW orderHigh temperatureSuperconductor Fermi liquidwith “large”Fermi surfacesDavisTuesday, January 17, 2012


D.J. Scalapino, E. Loh, and J.E. Hirsch, Phys. Rev. B 34, 8190 (1986)Ar. Abanov, A. V. Chubukov, and A. M. Finkel'stein, Europhys. Lett. 54, 488 (2001)S. Raghu, S.A. Kivelson, and D.J. Scalapino, Phys. Rev. B 81, 224505 (2010)M. A. Metlitski and S. Sachdev, Phys. Rev. B 85, 075127 (2010)TAF metalwith “small”Fermi pocketsIncreasing SDW orderStrangeMetalwith long-rangeentanglementHigh temperatureSuperconductor Fermi liquidwith “large”Fermi surfacesDavisTuesday, January 17, 2012


Challenge to string theory:Describe quantum critical points and phases ofmetallic systemsTuesday, January 17, 2012


Challenge to string theory:Describe quantum critical points and phases ofmetallic systemsCan we obtain holographic theoriesof superconductors andordinary metals (Fermi liquids)?Tuesday, January 17, 2012


Challenge to string theory:Describe quantum critical points and phases ofmetallic systemsCan we obtain holographic theoriesof superconductors andordinary metals (Fermi liquids)?YesTuesday, January 17, 2012


Challenge to string theory:Describe quantum critical points and phases ofmetallic systemsDoes holography yield metals other thanordinary metals ?Tuesday, January 17, 2012


Challenge to string theory:Describe quantum critical points and phases ofmetallic systemsDoes holography yield metals other thanordinary metals ?Yes, lots of them, with many “strange”properties !Tuesday, January 17, 2012


Challenge to string theory:Describe quantum critical points and phases ofmetallic systemsDo any of the holographic “strange metals” havethe correct type of long-range entanglement ?Tuesday, January 17, 2012


Challenge to string theory:Describe quantum critical points and phases ofmetallic systemsDo any of the holographic “strange metals” havethe correct type of long-range entanglement ?Yes, a very select subset has the properlogarithmic violation of the area law ofentanglement entropy !!These are now being studied intensively.........N. Ogawa, T. Takayanagi, and T. Ugajin, arXiv:1111.1023; L. Huijse, S. Sachdev, B. Swingle, arXiv:1112.0573Tuesday, January 17, 2012


ConclusionsPhases of matter with long-rangequantum entanglement areprominent in numerous modernmaterials.Tuesday, January 17, 2012


ConclusionsSimplest examples of long-rangeentanglement are atquantum-critical points of insulatingantiferromagnetsTuesday, January 17, 2012


ConclusionsMore complex examples in metallicstates are experimentallyubiquitous, but pose difficultstrong-coupling problems toconventional methods of fieldtheoryTuesday, January 17, 2012


ConclusionsString theory and holography offera remarkable new approach todescribing states with long-rangequantum entanglement.Tuesday, January 17, 2012


ConclusionsString theory and holography offera remarkable new approach todescribing states with long-rangequantum entanglement.Much recent progress offers hope of aholographic description of “strange metals”Tuesday, January 17, 2012

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