An absolutely incredible, highly interconnected web of ideas connecting some of the most important discoveries of late twentieth century physics and mathematics. This is an extremely abridged, biased history (1970-2010) with many truly ground-breaking works still not mentioned:
1971: Wegner reformulates the Ising model as a Z/2 gauge theory and discovers phase transitions without local order parameters (beginning of understanding of topological order).
1973: Anderson proposes resonating valence bonds (quantum spin liquids) as a phase of matter in quantum magnets, generalizing Linus Paulings' resonating valence bond description of ammonium.
1974: Chern,Simons construct the Chern-Simons form and associated invariant in odd dims
1974: Chern,Simons construct the Chern-Simons form and associated invariant in odd dims
1976: Jackiw and Rebbi show that the one-dimensional Dirac equation with a domain wall mass has a half-charge zero mode.
1977: Leinaas and Myrheim suggest possibility of fractional quantum statistics in 2 spatial dimensions
1977: Leinaas and Myrheim suggest possibility of fractional quantum statistics in 2 spatial dimensions
1980: Y. Manin proposes idea of a quantum computer in a book, "Computable and Noncomputable"
1980: von Klitzing discovers the integer quantum Hall (IQH) effect in GaAs/AlGaAs heterostructures, eventually leading to a new resistance standard
1980: von Klitzing discovers the integer quantum Hall (IQH) effect in GaAs/AlGaAs heterostructures, eventually leading to a new resistance standard
1981: Laughlin explains integer quantized Hall conductance using gauge invariance and flux insertion
1982: Halperin explains integer quantized Hall conductance and chiral edge theory of IQH states
1982: Halperin explains integer quantized Hall conductance and chiral edge theory of IQH states
1982: Thouless, Kohmoto, Nightingale, de Nijs (TKNN) relate integer quantized Hall conductance to a topological invariant of band structures
1982: Feynman publishes essay on simulating physics with quantum computers
1982: Feynman publishes essay on simulating physics with quantum computers
1982: Tsui, Stormer, Gossard discover the fractional quantum Hall (FQH) effect in GaAs/AlGaAs heterostructures
1982: Wilczek suggests fractional statistics particles as arising from charge-flux bound states in two spatial dimensions, coins term "anyon"
1982: Wilczek suggests fractional statistics particles as arising from charge-flux bound states in two spatial dimensions, coins term "anyon"
1983: Simon points out that the TKNN invariant is a Chern number, establishing a connection between topology of fiber bundles discovered in 1940s and quantum condensed matter physics.
1983: Laughlin explains the filling 1/3 FQH state, theoretically discovers existence of fractionally charged quasiparticles
1983: Donaldson discovers new topological invariants of 4-manifolds using instantons and gauge theory
1983: Donaldson discovers new topological invariants of 4-manifolds using instantons and gauge theory
1983-1984: Michael Berry explains geometric phases for adiabatic evolution in quantum mechanics
1984: Belavin, Polyakov, Zamalodchikov describe conformal field theory and the infinite dimensional Virasoro algebra in 2 dimensions
1984: Belavin, Polyakov, Zamalodchikov describe conformal field theory and the infinite dimensional Virasoro algebra in 2 dimensions
1984: Jones discovers the "Jones polynomial," a new invariant of knots (an exponentially difficult computation given a knot).
1984: Halperin shows Laughlin quasiparticles in FQH states carry fractional statistics (can be defined through Berry phase from adiabatic braiding).
1984: Halperin shows Laughlin quasiparticles in FQH states carry fractional statistics (can be defined through Berry phase from adiabatic braiding).
1986: Bednorz and Muller discover high temperature superconductivity in cuprates
1987: Anderson proposes resonating valence bonds (RVB), i.e. quantum spin liquids, as an explanation of high temperature superconductivity arising from a doped Mott insulator
1987: Anderson proposes resonating valence bonds (RVB), i.e. quantum spin liquids, as an explanation of high temperature superconductivity arising from a doped Mott insulator
1987: Baskaran, Zou, Anderson show how gauge theory can emerge from a projection to states with one electron per site (Gutzwiller projection), developing slave particle mean field theory of RVB states.
1987: Kivelson, Rokhsar, Sethna discuss topological order of the RVB state
1987: Kivelson, Rokhsar, Sethna discuss topological order of the RVB state
1987: Kalmeyer and Laughlin point out equivalence between RVB and FQH states.
1987: Willett, Eisenstein, et. al. discover first even-denominator FQH state at filling fraction 5/2.
1987: Willett, Eisenstein, et. al. discover first even-denominator FQH state at filling fraction 5/2.
1988: Moore and Seiberg develop a new mathematical structure, unitary modular tensor categories (UMTCs), to describe rational conformal field theories
1988: Witten introduces topological quantum field theory (TQFT) by "twisting" supersymmetric Yang-Mills theory, providing a new way of understanding Donaldson's invariants using quantum field theory
1988: Atiyah mathematically defines topological quantum field theory (TQFT)
1988: Atiyah mathematically defines topological quantum field theory (TQFT)
1988: Haldane shows how integer quantum Hall effect can occur without a magnetic field
1989: Witten develops Chern-Simons theory as a TQFT, giving the first intrinsically three-dimensional explanation of the Jones polynomial and discovering new "quantum" invariants of 3-manifolds. Connects CS theory to conformal field theory as a bulk-boundary correspondence.
1989: Zhang, Hansson, Kivelson develop Chern-Simons theory as effective field theory of FQH states
1989-1990: Wen discovers that chiral quantum spin liquids and FQH states possess topological order and topologically protected degeneracies. Develops chiral conformal field theory description of FQH edge. Connects Moore-Seiberg-Witten results to condensed matter physics.
1991: Moore-Read propose non-Abelian statistics to explain 5/2 FQH effect. Demonstrate how many-electron wave functions can be obtained as a correlation function of vertex operators in a chiral conformal field theory. Build on Moore-Seiberg-Witten insights.
1991: Wen proposes non-Abelian statistics in a general class of FQH states using Witten's non-Abelian CS theory results combined with slave particle mean field theory methods (used previously for RVB states).
1991: Read and Sachdev establish through large N expansion that quantum spin liquids with topological order (RVB) can arise in frustrated quantum magnets
1992: Turaev and Viro introduce a path integral in terms of a state sum by taking as input a special fusion category, leading to new quantum invariants of 3-manifolds and generalizing Witten's quantum invariants.
1994: Kane-Fisher use Wen's edge theory of FQH to propose measuring fractional electric charge through shot noise.
1995: Shor discovers quantum error correcting codes
1997: de-Picciotto et. al. directly measure fractional electric charge through shot noise in FQH systems.
1995: Shor discovers quantum error correcting codes
1997: de-Picciotto et. al. directly measure fractional electric charge through shot noise in FQH systems.
1997: Chamon, Freed, Kivelson, Sondhi, Wen propose to measure fractional statistics in FQH states using a Fabry-Perot interferometer.
1997: Kitaev establishes connection between quantum error correction and topologically ordered phases of matter. Points out that topologically protected degeneracies can be used as protected logical qubits.
Shows how Wegner's Z/2 gauge theory can arise from an exactly solvable model of qubits (the toric code). Settles long debate about whether quantum spin liquids can exist in principle by providing an exactly solvable Hamiltonian.
1997: Altland and Zirnbauer generalize the Wigner-Dyson classification of symmetries to describe disordered mesoscopic superconductors.
1998: Bravyi and Kitaev adapt the toric code to the surface code, creating a topologically protected qubit by alternating topological boundary conditions.
1998: Freedman and Meyer show how Kitaev's toric code, when formulated on a 9-edge cellulation of the projective plane, is the same as Shor's 9 qubit quantum error correcting code, deepening the connection between topological quantum matter and quantum error correction.
1999: Read-Green show that two-dimensional p+ip superconductors host Majorana zero modes at their vortex cores, providing a new route to non-Abelian statistics and topological degeneracies. Related to the Jackiw-Rebbi zero mode discovered in 1976.
2000: Kitaev notices that one-dimensional superconductors can give rise to Majorana zero modes and therefore a topologically protected degeneracy. Provides crucial new insight on Jordan-Wigner duality of the 2-dimensional Ising model.
2000: Freedman, Larsen, Wang demonstrate a topological quantum field theory where the braiding of non-Abelian anyons gives universal quantum computation.
2001: Dennis, Kitaev, Landahl, Preskill study the surface code as as topological quantum memory. Discover error threshold ~ 1% for quantum error correction, suggesting fault-tolerant quantum computation may be practical.
2005: Kane and Mele discover a new Z/2 topological invariant in two dimensions, related to two time-reversed copies of Haldane's model, generalizing the TKNN / Chern number invariant to cases with time-reversal symmetry.
2005: Levin and Wen define the string-net models, providing a Hamiltonian realization of the Turaev-Viro topological quantum field theories, and eventually leading to the most general known class of two-dimensional quantum error correcting codes.
2005: Microsoft Research Station Q founded to explore topological quantum computation
2005: Das Sarma, Freedman, Nayak propose topological qubit using the 5/2 FQH effect. Microsoft funds pursuit of topological qubit using 5/2 FQH effect.
2006: Bernevig, Hughes, and Zhang propose realizing the Kane-Mele Z/2 topological insulator in HgTe quantum wells.
2006: Bonderson, Kitaev, and Shtengel and independently Halperin and Stern propose to measure non-Abelian statistics in the 5/2 FQH effect using an interfemeter
2006: Bonderson, Kitaev, and Shtengel and independently Halperin and Stern propose to measure non-Abelian statistics in the 5/2 FQH effect using an interfemeter
2007: Moore, Balents; Roy; Fu, Kane, Mele generalize the Z/2 topological invariant to 3 dimensional topological insulators.
2007: Konig et. al. report experimental observation of topological insulators in HgTe quantum wells.
2007: Konig et. al. report experimental observation of topological insulators in HgTe quantum wells.
2008: Fu and Kane apply the Read-Green theory to show how Majorana zero modes can arise at the surface of a three-dimensional Z/2 topological insulator coupled to an s-wave superconductor, removing need for an odd parity superconductor.
2008-2009: Schnyder, Ryu, Furusaki, Ludwig classify free fermion topoological insulators and superconductors using nonlinear sigma models with topological terms, using the Altland-Zirnbauer classification.
2009: Kitaev provides periodic table of free fermion topological insulators and superconductors using K-theory.
2009: Xia et. al. report experimental observation of single Dirac cone at surface of Bi2Se3, reported to be a doped topological insulator.
2009: Xia et. al. report experimental observation of single Dirac cone at surface of Bi2Se3, reported to be a doped topological insulator.
2010: Sau, Lutchyn, das Sarma suggest how simple semiconductor-superconductor heterostructures can provide physical realization of Majorana zero modes, removing need for topological insulator.
2010: Lutchyn, Sau, das Sarma and independently Oreg, Refael, von Oppen, propose a way to realize Kitaev's Majorana nanowire by proximitizing a spin-orbit coupled semiconductor nanowire to an s-wave superconductor with a magnetic field.
2010: Microsoft Station Q changes course to pursue experimental realization of Majorana nanowires for purposes of topological quantum computation.
Correction: von Kitzing discovered IQH in Si-MOSFETs
correction: benzene is described by resonating valence bonds. not sure about ammonium
