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There is controversy whether dusty starbursts selected at submillimeterwavelengths can trace galaxy overdensities. We perform the first systematicsearch for protoclusters around a homogeneously selected sample of 12spectroscopically confirmed submillimeter galaxies (SMGs) at $z\sim1.2-5.3$ inthe GOODS-N field. We applied the Poisson Probability Method (PPM) to searchfor Mpc scale overdensities around these SMGs using three photometric redshiftcatalogs. We detect galaxy overdensities for 11 out of the 12 SMGs($92\%\pm8$\%), distributed over eight protoclusters. We confirm threepreviously discovered protoclusters, and we detect five new ones around theSMGs SMMJ123634 ($z=1.225$), ID.19 ($z=2.047$), SMMJ123607 ($z=2.487$),SMMJ123606 ($z=2.505$), and GN10 ($z=5.303$). A wavelet-based analysis showsthat the SMGs live in protocluster cores with a complex morphology (compact,filamentary, or clumpy) and an average size of $\sim(0.4-1)$Mpc. By comparingthe PPM results obtained using independently the three redshift catalogs, wepossibly witness a transitioning phase at $z\gtrsim4$ for the galaxypopulations. While $z\lesssim4$ protoclusters appear to be populated by dustygalaxies, those at highest redshifts $z\sim5$ are detected as overdensities ofLyman$\alpha$ emitters or Lyman break galaxies. We also find a good correlationbetween the molecular (H$_2$) gas mass of the SMG and the overdensitysignificance. To explain the overall phenomenology, we suggest that galaxyinteractions in dense environments likely triggered the starburst and gas-richphase of the SMGs. Altogether, we support the scenario that SMGs are excellenttracers of distant protoclusters. Those presented in this work are excellenttargets for the {\it James Webb Space Telescope.} Surveys with forthcomingfacilities (e.g., {\it Euclid}, LSST) can be tuned to detect even largersamples of distant protoclusters.

Bright submillimeter galaxies do trace galaxy protoclusters