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Quantum Entanglement,Strange metals,and black holesSubir Sachdev, Harvard University
Quantum Entanglement,Strange metals,and black holesSuperconductor, levitated by an unseen magnet, in which countlesstrillions of electrons form a vast interconnected quantum state.Scientific American, January 2013Subir Sachdev, Harvard University
SCIENCESorry, Einstein. Quantum Study Suggests‘Spooky Action’ Is Real.By JOHN MARKOFFOCT. 21, 2015In a landmark study, scientists at Delft University of Technology in theNetherlands reported that they had conducted an experiment that they say provedone of the most fundamental claims of quantum theory — that objects separated bygreat distance can instantaneously affect each other’s behavior.The finding is another blow to one of the bedrock principles of standardPart ofinfluencedthe laboratoryphysics known as “locality,” which states that an object is directlyonlyfor an inexperimentby its immediate surroundings. The Delft study, publishedsetupWednesdaytheat DelftUniversityofjournal Nature, lends further credence to an idea that Einsteinfamouslyrejected.Technology, in whichHe said quantum theory necessitated “spooky action at a distance,” and he refusedtwo diamonds were setto accept the notion that the universe could behave in such a1.3strangeand apart,kilometersapparently random fashion.entangled and thenshared information.In particular, Einstein derided the idea that separate particles could be
QuantumentanglementQuantum phase transitions
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentTWO SLITS Interference of water waves
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentBullets
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentSend electrons through the slits
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentInterference of electrons
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentIs the electron a wave ?Interference of electrons
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentTWO SLITS Unlike water waves, electrons arriveone-by-one (so is it like a particle ?)Interference of electrons
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentBut if it islike aparticle,which slitdoes eachelectron passthrough ?Interference of electrons
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentBut if it islike aparticle,which slitdoes eachelectron passthrough ?Nointerferencewhen youwatch theelectronsInterference of electrons
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentBut if it islike aparticle,which slitdoes eachelectron passthrough ?Eachelectronpassesthroughboth slits !Interference of electrons
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentLet L represent the statewith the electron in the left slit L
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentLet L represent the statewith the electron in the left slit L RAnd R represents the statewith the electron in the right slit
Principles of Quantum Mechanics: 1. Quantum SuperpositionThe double slit experimentLet L represent the statewith the electron in the left slit L RAnd R represents the statewith the electron in the right slitActual state of each electron is Li Ri
Principles of Quantum Mechanics: 1I. Quantum EntanglementQuantum Entanglement: quantum superpositionwith more than one particle
Principles of Quantum Mechanics: 1I. Quantum EntanglementQuantum Entanglement: quantum superpositionwith more than one particleHydrogen atom:
Principles of Quantum Mechanics: 1I. Quantum EntanglementQuantum Entanglement: quantum superpositionwith more than one particleHydrogen atom:Hydrogen molecule: 1 ( 2 )
Principles of Quantum Mechanics: 1I. Quantum EntanglementQuantum Entanglement: quantum superpositionwith more than one particle
Principles of Quantum Mechanics: 1I. Quantum EntanglementQuantum Entanglement: quantum superpositionwith more than one particle
Principles of Quantum Mechanics: 1I. Quantum EntanglementQuantum Entanglement: quantum superpositionwith more than one particle
Principles of Quantum Mechanics: 1I. Quantum EntanglementQuantum Entanglement: quantum superpositionwith more than one particleEinstein-Podolsky-Rosen “paradox” (1935):Measurement of one particle instantaneouslydetermines the state of the other particlearbitrarily far away
QuantumentanglementQuantum phase transitions
QuantumentanglementBlackholesQuantum phase transitions
Black HolesObjects so dense that light isgravitationally bound to them.In Einstein’s theory, theregion inside the black holehorizon is disconnected fromthe rest of the universe.2GMHorizon radius R 2c
On September 14, 2015, LIGO detected the merger oftwo black holes, each weighing about 30 solar masses,with radii of about 100 km, 1.3 billion light years away
On September 14, 2015, LIGO detected the merger oftwo black holes, each weighing about 30 solar masses,with radii of about 100 km, 1.3 billion light years away0.1 seconds later !
LIGOSeptember 14, 2015
Black Holes Quantum theoryAround 1974, Bekenstein and Hawkingshowed that the application of thequantum theory across a black holehorizon led to many astonishingconclusions
Quantum Entanglement across a black hole horizon
Quantum Entanglement across a black hole horizonBlack holehorizon
Quantum Entanglement across a black hole horizonBlack holehorizon
Quantum Entanglement across a black hole horizonThere is long-range quantumentanglement between the insideand outside of a black holeBlack holehorizon
Quantum Entanglement across a black hole horizonHawking used this to show thatblack hole horizons have anentropy and a temperatureBlack holehorizon
Quantum Entanglement across a black hole horizonHawking used this to show thatblack hole horizons have anentropy and a temperature(because to an outside observer, the state of theelectron inside the black hole is an unknown)Black holehorizon
LIGOSeptember 14, 2015 The Hawking temperature, TH influences the radiation from theblack hole at the very last stages of the ring-down (not observedso far). The ring-down (approach to thermal equilibrium) hap pens very rapidly in a time 8 milliseconds.k B TK
QuantumentanglementBlackholesQuantum phase transitions
QuantumentanglementStrangemetalsBlackholesQuantum phase transitions
High temperaturesuperconductorsYBa2 Cu3 O6 x
Nd-Fe-B magnets,YBaCuO superconductorJulian Hetel and Nandini Trivedi, Ohio State University
Slide by J. C. Seamus DavisPower Efficiency/Capacity/StabilityPower BottlenecksEfficient Rotating MachinesInformation TechnologyHE AcceleratorsUltra-High Magnetic FieldsAccommodate Renewable PowerNext Generation HEPScience / MedicineMedicalTransport
High temperaturesuperconductorsYBa2 Cu3 O6 x
AntiferromagnetStrange metalSMSuperconductorFLp (hole/Cu)Figure: K. Fujita and J. C. Seamus Davis
AntiferromagnetStrange metalSMFLSpins of electrons on Cu sitesp (hole/Cu)Figure: K. Fujita and J. C. Seamus Davis
Square lattice of Cu sites
Square lattice of Cu sitesRemove densityp electrons
Square lattice of Cu sitesElectronsentangle in(“Cooper”)pairs intochemical bonds
Square lattice of Cu sitesSuperconductivityCooper pairsform quantumsuperpositionsat in which allpairs are“everywhere atthe same time”
Square lattice of Cu sitesSuperconductivityCooper pairsform quantumsuperpositionsat in which allpairs are“everywhere atthe same time”
Square lattice of Cu sitesSuperconductivityCooper pairsform quantumsuperpositionsat in which allpairs are“everywhere atthe same time”
Square lattice of Cu sitesSuperconductivityCooper pairsform quantumsuperpositionsat in which allpairs are“everywhere atthe same time”
Square lattice of Cu sitesHigh temperature superconductivity !Electronsentangle byexchangingpartners, andthere is longrangequantumentanglementin the strangemetal.
Square lattice of Cu sitesHigh temperature superconductivity !Electronsentangle byexchangingpartners, andthere is longrangequantumentanglementin the strangemetal.
Square lattice of Cu sitesHigh temperature superconductivity !Electronsentangle byexchangingpartners, andthere is longrangequantumentanglementin the strangemetal.
Square lattice of Cu sitesHigh temperature superconductivity !Electronsentangle byexchangingpartners, andthere is longrangequantumentanglementin the strangemetal.
Square lattice of Cu sitesHigh temperature superconductivity !Electronsentangle byexchangingpartners, andthere is longrangequantumentanglementin the strangemetal.
Square lattice of Cu sitesHigh temperature superconductivity !Electronsentangle byexchangingpartners, andthere is longrangequantumentanglementin the strangemetal.
Square lattice of Cu sitesHigh temperature superconductivity !Electronsentangle byexchangingpartners, andthere is longrangequantumentanglementin the strangemetal.
Strange metalSMFLp (hole/Cu)Entangledelectrons lead to“strange”temperaturedependence ofresistivity andother propertiesFigure: K. Fujita and J. C. Seamus Davis
Almost all many-electron systems are described by thequasiparticle concept: a quasiparticle is an “excitedlump” in the many-electron state which responds justlike an ordinary particle.R.D. Mattuck
Almost all many-electron systems are described by thequasiparticle concept: a quasiparticle is an “excitedlump” in the many-electron state which responds justlike an ordinary particle.Quasiparticles eventually collide with each other.Such collisions eventually leads to thermalequilibration in a chaotic quantum state, but theequilibration takes a long time.
Quantum matter without quasiparticlesThe complex quantum entanglement in the strangemetal does not allow for any quasiparticle excitations.
Quantum matter without quasiparticlesThe complex quantum entanglement in the strangemetal does not allow for any quasiparticle excitations. Systems without quasiparticles, like the strange metal,reach quantum chaos much more quickly than those without quasiparticles. There is an lower bound on the phase coherence time ( ' ),and the time to many-body quantum chaos ( L ) in allmany-body quantum systems: ' L CkB T 2 kB T(SS, 1999)(Maldacena, Shenker, Stanford, 2015) In the strange metal the above inequalities become equalities as T ! 0.
Quantum matter without quasiparticlesThe complex quantum entanglement in the strangemetal does not allow for any quasiparticle excitations. Systems without quasiparticles, like the strange metal,reach quantum chaos much more quickly than those without quasiparticles. There is an lower bound on the phase coherence time ( ' ),and the time to many-body quantum chaos ( L ) in allmany-body quantum systems: ' L CkB T 2 kB T(SS, 1999)(Maldacena, Shenker, Stanford, 2015) In the strange metal the above inequalities become equalities as T ! 0.
Quantum matter without quasiparticlesThe complex quantum entanglement in the strangemetal does not allow for any quasiparticle excitations. Systems without quasiparticles, like the strange metal,reach quantum chaos much more quickly than those without quasiparticles. There is an lower bound on the phase coherence time ( ' ),and the time to many-body quantum chaos ( L ) in allmany-body quantum systems: ' L CkB T 2 kB T(SS, 1999)(Maldacena, Shenker, Stanford, 2015) In the strange metal the above inequalities become equalities as T ! 0.
QuantumentanglementStrangemetalsBlackholesQuantum phase transitions
QuantumentanglementStrangemetalsBlackholesA “toy model” which is both astrange metal and a black hole!Quantum phase transitions
The Sachdev-Ye-Kitaev (SYK) modelPick a set of random positions
The Sachdev-Ye-Kitaev (SYK) modelPlace electrons randomly on some sites
The Sachdev-Ye-Kitaev (SYK) modelEntangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) modelEntangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) modelEntangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) modelEntangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) modelEntangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) modelEntangle electrons pairwise randomly
The Sachdev-Ye-Kitaev (SYK) modelThe SYK model has “nothing but entanglement”
The Sachdev-Ye-Kitaev (SYK) modelThis describes both a strange metal and a black hole!
SYK model1H (2N )3/2NX† †Jij;k ci cj ck c µ†ci ciii,j,k, 1ci cj cj ci 0X†ci c j, 1 X †Q ci ciN i†cj ci ijJij;k are independent random variables with Jij;k 0 and Jij;k 2 J 2N ! 1 yields critical strange metal.SS and J.Ye 1993A. Kitaev, (2015) ; SS 2015
SYK and black holes x
SYK and black holesBlack holehorizon xThe SYK model has “dual” descriptionin which an extra spatial dimension, , emerges.The curvature of this “emergent” spacetime is describedby Einstein’s theory of general relativity
SYK and black holesBlack holehorizon An extra spatialdimension emerges fromquantum entanglement! xSS 2010; A. Kitaev, 2015
SYK and black holesBlack holehorizon xBoth the SYK modeland the theory of gravity have a time to quantum chaos 2 kB TA. Kitaev, 2015Maldacena, Stanford 2016
Tensor network ofhierarchical entanglement depth ofentanglement xD-dimensionalspace
String theory neara “D-brane” depth of spatial directionEmergententanglementof SYK model or string theory xD-dimensionalspace
String theory neara “D-brane” xQuantum entanglementleads to an emergentspatial dimensiondepth of spatial directionEmergententanglementof SYK model or string theoryD-dimensionalspace
QuantumentanglementStrangemetalsBlackholesA “toy model” which is both astrange metal and a black hole!Quantum phase transitions
Quantum Entanglement,Strange metals,and black holesSubir Sachdev, Harvard University and TIFR
physics known as “locality,” which states that an object is directly influenced only by its immediate surroundings. The Delft study, published Wednesday in the journal Nature, lends further credence to an idea that Einstein famously rejected. He said quantum theory n
