**Quantum** **entanglement****and** **the** **phases** **of** **matter**TIFR, 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 **the**oryEntanglement **and** emergent dimensions2. High temperature superconductors**and** strange metalsHolography **of** compressible quantum **phases**Tuesday, January 17, 2012

Outline1. **Quantum** critical points **and** string **the**oryEntanglement **and** emergent dimensions2. High temperature superconductors**and** strange metalsHolography **of** compressible quantum **phases**Tuesday, 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 o**the**r.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 3**Quantum** 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 Norm**and**, 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** **the**quantum paramagnet00 0.5 1 1.5 2 2.5 3Pressure [kbar]Tuesday, January 17, 2012Christian Ruegg, Bruce Norm**and**, 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 above**the** Néel state0.200 0.5 1 1.5 2 2.5 3Pressure [kbar]Tuesday, January 17, 2012Christian Ruegg, Bruce Norm**and**, 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 Norm**and**, 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 **the**oretically predicted energyS. Sachdev, arXiv:0901.4103Tuesday, January 17, 2012Christian Ruegg, Bruce Norm**and**, 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 cλ**Quantum** critical point with non-local**entanglement** in spin wavefunctionTuesday, January 17, 2012

Tensor network representation **of** **entanglement**at quantum critical pointD-dimensionalspacedepth **of****entanglement**Tuesday, January 17, 2012

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

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

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

String **the**ory• Allows unification **of** **the** st**and**ard 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 **the**ory on a D-brane is an ordinary quantumfield **the**ory with no gravity.• In D = 2, we obtain strongly-interacting CFT3s. These are“dual” to string **the**ory 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 **the**ory on a D-brane is an ordinary quantumfield **the**ory with no gravity.• In D = 2, we obtain strongly-interacting CFT3s. These are“dual” to string **the**ory on anti-de Sitter space: AdS4.Tuesday, January 17, 2012

Tensor network representation **of** **entanglement**at quantum critical pointD-dimensionalspacedepth **of****entanglement**Tuesday, 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 **the**ory neara D-braneD-dimensionalspaceEmergent depth **of** direction**entanglement** **of** AdS4Tuesday, January 17, 2012

Tensor network representation **of** **entanglement**at quantum critical pointD-dimensionalspaceEmergent depth **of** direction**entanglement** **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 **of****entanglement**Tuesday, January 17, 2012

Entanglement entropyAD-dimensionalspaceDraw a surface which intersects **the** minimal number **of** linksEmergent depth **of** direction**entanglement** **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+1**Quantum****matter** withlong-range**entanglement**rEmergent holographic directionJ. McGreevy, arXiv0909.0518Tuesday, January 17, 2012

AdS d+2 R d,1MinkowskiCFT d+1A**Quantum****matter** withlong-range**entanglement**rEmergent holographic directionTuesday, January 17, 2012

AdS d+2 R d,1MinkowskiCFT d+1Areameasures**entanglement**entropyrAEmergent holographic direction**Quantum****matter** withlong-range**entanglement**Tuesday, January 17, 2012

= √ 1 ↑↓ − ↓↑2λ cλ**Quantum** critical point with non-local**entanglement** 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).**Quantum**criticalClassicalspinwavesDilutetriplongasNeel 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).**Quantum**criticalClassicalspinwavesDilutetriplongasNeel 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).**Quantum**criticalClassicalspinwavesDilutetriplongasShort-range**entanglement**Short-range**entanglement**Neel 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).**Quantum**criticalClassicalspinwavesDilutetriplongasNeel 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 **entanglement****Quantum**criticalClassicalspinwavesDilutetriplongasNeel 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 **of**2+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 **of**2+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 **of**2+1 dimensionalquantum criticalsystemProvides successful description**of** many properties **of** quantumcritical points at non-zerotemperaturesTuesday, January 17, 2012

Outline1. **Quantum** critical points **and** string **the**oryEntanglement **and** emergent dimensions2. High temperature superconductors**and** strange metalsHolography **of** compressible quantum **phases**Tuesday, January 17, 2012

**Quantum** critical points **and** string **the**oryEntanglement **and** emergent dimensions2. High temperature superconductors**and** strange metalsHolography **of** compressible quantum **phases**Tuesday, 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 **entanglement**Tuesday, 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, **and**R. 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, **and**R. L. Short-range Greene, Rev. Mod. **entanglement**Phys. 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, **and**R. 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, **and**R. 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, **and**R. 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, **and**R. 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. N**and**i, M. G. Kim, A. Kreyssig, R. M. Fern**and**es, 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** **the**iron 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** **the**iron 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 **entanglement**Physical Review B 81, 184519 (2010)

Temperature-doping phase diagram **of** **the**iron 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** **the**iron 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** **the**iron 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** **the**iron pnictides:Excitations **of** a ground statewith long-range **entanglement**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-pressure phase diagram **of**an 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 **of**th interac**of****the** 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 transio**the** para-Tuesday, January 17, 2012Temperature-pressure phase diagram **of**an heavy-fermion superconductor

Ordinary metals (Fermi liquids)Metal with “large”Fermi surfaceMomenta wi**the**lectron statesoccupiedMomenta wi**the**lectron 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 electron**and** hole pocketsMetal with “large”Fermi surfaceIncreasing interactionFermi surface reconstruction **and**onset **of** antiferromagnetismTuesday, January 17, 2012

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

Fermi surface+antiferromagnetismIncreasing SDW orderAFϕ =0**Quantum** criticalpoint realizes astrongly-coupled“strange metal”with long-rangeϕ =0 **entanglement** !Metal with electron**and** hole pocketsMetal with “large”Fermi surfaceIncreasing interactionFermi surface reconstruction **and**onset **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-range**entanglement**High temperatureSuperconductor Fermi liquidwith “large”Fermi surfacesDavisTuesday, January 17, 2012

Challenge to string **the**ory:Describe quantum critical points **and** **phases** **of**metallic systemsTuesday, January 17, 2012

Challenge to string **the**ory:Describe quantum critical points **and** **phases** **of**metallic systemsCan we obtain holographic **the**ories**of** superconductors **and**ordinary metals (Fermi liquids)?Tuesday, January 17, 2012

Challenge to string **the**ory:Describe quantum critical points **and** **phases** **of**metallic systemsCan we obtain holographic **the**ories**of** superconductors **and**ordinary metals (Fermi liquids)?YesTuesday, January 17, 2012

Challenge to string **the**ory:Describe quantum critical points **and** **phases** **of**metallic systemsDoes holography yield metals o**the**r thanordinary metals ?Tuesday, January 17, 2012

Challenge to string **the**ory:Describe quantum critical points **and** **phases** **of**metallic systemsDoes holography yield metals o**the**r thanordinary metals ?Yes, lots **of** **the**m, with many “strange”properties !Tuesday, January 17, 2012

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

Challenge to string **the**ory:Describe quantum critical points **and** **phases** **of**metallic systemsDo any **of** **the** holographic “strange metals” have**the** correct type **of** long-range **entanglement** ?Yes, a very select subset has **the** properlogarithmic violation **of** **the** area law **of****entanglement** 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-range**entanglement** are atquantum-critical points **of** insulatingantiferromagnetsTuesday, January 17, 2012

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

ConclusionsString **the**ory **and** holography **of**fera remarkable new approach todescribing states with long-rangequantum **entanglement**.Tuesday, January 17, 2012

ConclusionsString **the**ory **and** holography **of**fera remarkable new approach todescribing states with long-rangequantum **entanglement**.Much recent progress **of**fers hope **of** aholographic description **of** “strange metals”Tuesday, January 17, 2012